Geometric Inequalities

Author : Yurii D. Burago,Viktor A. Zalgaller
Publisher : Springer Science & Business Media
Page : 346 pages
File Size : 46,9 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9783662074411

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Geometric Inequalities by Yurii D. Burago,Viktor A. Zalgaller Pdf

A 1988 classic, covering Two-dimensional Surfaces; Domains on the Plane and on Surfaces; Brunn-Minkowski Inequality and Classical Isoperimetric Inequality; Isoperimetric Inequalities for Various Definitions of Area; and Inequalities Involving Mean Curvature.

Author : Dragoslav S. Mitrinovic,J. Pecaric,V. Volenec
Publisher : Springer Science & Business Media
Page : 728 pages
File Size : 50,8 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9789401578424

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Recent Advances in Geometric Inequalities by Dragoslav S. Mitrinovic,J. Pecaric,V. Volenec Pdf

Author : Hayk Sedrakyan,Nairi Sedrakyan
Publisher : Springer
Page : 452 pages
File Size : 53,5 Mb
Release : 2017-05-27
Category : Mathematics
ISBN : 9783319550800

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Geometric Inequalities by Hayk Sedrakyan,Nairi Sedrakyan Pdf

This unique collection of new and classical problems provides full coverage of geometric inequalities. Many of the 1,000 exercises are presented with detailed author-prepared-solutions, developing creativity and an arsenal of new approaches for solving mathematical problems. This book can serve teachers, high-school students, and mathematical competitors. It may also be used as supplemental reading, providing readers with new and classical methods for proving geometric inequalities.

Author : Themistocles RASSIAS,Hari M. Srivastava
Publisher : Springer Science & Business Media
Page : 377 pages
File Size : 55,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401145770

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Analytic and Geometric Inequalities and Applications by Themistocles RASSIAS,Hari M. Srivastava Pdf

Analytic and Geometric Inequalities and Applications is devoted to recent advances in a variety of inequalities of Mathematical Analysis and Geo metry. Subjects dealt with in this volume include: Fractional order inequalities of Hardy type, differential and integral inequalities with initial time differ ence, multi-dimensional integral inequalities, Opial type inequalities, Gruss' inequality, Furuta inequality, Laguerre-Samuelson inequality with extensions and applications in statistics and matrix theory, distortion inequalities for ana lytic and univalent functions associated with certain fractional calculus and other linear operators, problem of infimum in the positive cone, alpha-quasi convex functions defined by convolution with incomplete beta functions, Chebyshev polynomials with integer coefficients, extremal problems for poly nomials, Bernstein's inequality and Gauss-Lucas theorem, numerical radii of some companion matrices and bounds for the zeros of polynomials, degree of convergence for a class of linear operators, open problems on eigenvalues of the Laplacian, fourth order obstacle boundary value problems, bounds on entropy measures for mixed populations as well as controlling the velocity of Brownian motion by its terminal value. A wealth of applications of the above is also included. We wish to express our appreciation to the distinguished mathematicians who contributed to this volume. Finally, it is our pleasure to acknowledge the fine cooperation and assistance provided by the staff of Kluwer Academic Publishers. June 1999 Themistocles M. Rassias Hari M.

Author : Gangsong Leng
Publisher : World Scientific Publishing Company
Page : 144 pages
File Size : 42,9 Mb
Release : 2015-10-21
Category : Mathematics
ISBN : 9789814696500

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Geometric Inequalities by Gangsong Leng Pdf

In China, lots of excellent maths students take an active interest in various maths contests and the best six senior high school students will be selected to form the IMO National Team to compete in the International Mathematical Olympiad. In the past ten years China's IMO Team has achieved outstanding results — they won the first place almost every year. The author is one of the coaches of China's IMO National Team, whose students have won many gold medals many times in IMO. This book is part of the Mathematical Olympiad Series which discusses several aspects related to maths contests, such as algebra, number theory, combinatorics, graph theory and geometry. The book elaborates on Geometric Inequality problems such as inequality for the inscribed quadrilateral, the area inequality for special polygons, linear geometric inequalities, etc.

Author : G. H. Hardy,J. E. Littlewood,George Pólya
Publisher : Cambridge University Press
Page : 344 pages
File Size : 52,9 Mb
Release : 1952
Category : Mathematics
ISBN : 0521358809

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Inequalities by G. H. Hardy,J. E. Littlewood,George Pólya Pdf

This classic of the mathematical literature forms a comprehensive study of the inequalities used throughout mathematics. First published in 1934, it presents clearly and lucidly both the statement and proof of all the standard inequalities of analysis. The authors were well-known for their powers of exposition and made this subject accessible to a wide audience of mathematicians.

Author : G.V. Milovanovic
Publisher : Springer Science & Business Media
Page : 518 pages
File Size : 43,6 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9789401590860

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Recent Progress in Inequalities by G.V. Milovanovic Pdf

This volume is dedicated to the late Professor Dragoslav S. Mitrinovic(1908-1995), one of the most accomplished masters in the domain of inequalities. Inequalities are to be found everywhere and play an important and significant role in almost all subjects of mathematics as well as in other areas of sciences. Professor Mitrinovic used to say: `There are no equalities, even in human life inequalities are always encountered.' This volume provides an extensive survey of the most current topics in almost all subjects in the field of inequalities, written by 85 outstanding scientists from twenty countries. Some of the papers were presented at the International Memorial Conference dedicated to Professor D.S. Mitrinovic, which was held at the University of Nis, June 20-22, 1996. Audience: This book will be of great interest to researchers in real, complex and functional analysis, special functions, approximation theory, numerical analysis and computation, and other fields, as well as to graduate students requiring the most up-to-date results.

Author : Nicholas D. Kazarinoff
Publisher : Mathematical Association of America (MAA)
Page : 148 pages
File Size : 48,9 Mb
Release : 1961
Category : Mathematics
ISBN : STANFORD:36105049304657

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Geometric Inequalities by Nicholas D. Kazarinoff Pdf

Anybody who liked their first geometry course (and some who did not) will enjoy the simply stated geometric problems about maximum and minimum lengths and areas in this book. Many of these already fascinated the Greeks, for example, the problem of enclosing the largest possible area by a fence of given length, and some were solved long ago; but others remain unsolved even today. Some of the solutions of the problems posed in this book, for example, the problem of inscribing a triangle of smallest perimeter into a given triangle, were supplied by world famous mathematicians, other by high school students.

Author : Radmila Bulajich Manfrino,José Antonio Gómez Ortega,Rogelio Valdez Delgado
Publisher : Springer Science & Business Media
Page : 220 pages
File Size : 48,9 Mb
Release : 2010-01-01
Category : Mathematics
ISBN : 9783034600507

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Inequalities by Radmila Bulajich Manfrino,José Antonio Gómez Ortega,Rogelio Valdez Delgado Pdf

This book is intended for the Mathematical Olympiad students who wish to prepare for the study of inequalities, a topic now of frequent use at various levels of mathematical competitions. In this volume we present both classic inequalities and the more useful inequalities for confronting and solving optimization problems. An important part of this book deals with geometric inequalities and this fact makes a big difference with respect to most of the books that deal with this topic in the mathematical olympiad. The book has been organized in four chapters which have each of them a different character. Chapter 1 is dedicated to present basic inequalities. Most of them are numerical inequalities generally lacking any geometric meaning. However, where it is possible to provide a geometric interpretation, we include it as we go along. We emphasize the importance of some of these inequalities, such as the inequality between the arithmetic mean and the geometric mean, the Cauchy-Schwarz inequality, the rearrangementinequality, the Jensen inequality, the Muirhead theorem, among others. For all these, besides giving the proof, we present several examples that show how to use them in mathematical olympiad problems. We also emphasize how the substitution strategy is used to deduce several inequalities.

Author : Isaac Chavel
Publisher : Cambridge University Press
Page : 292 pages
File Size : 53,8 Mb
Release : 2001-07-23
Category : Mathematics
ISBN : 0521802679

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Isoperimetric Inequalities by Isaac Chavel Pdf

This advanced introduction emphasizes the variety of ideas, techniques, and applications of the subject.

Author : Bruno Bianchini,Luciano Mari,Patrizia Pucci,Marco Rigoli
Publisher : Springer Nature
Page : 291 pages
File Size : 41,9 Mb
Release : 2021-01-18
Category : Mathematics
ISBN : 9783030627041

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Geometric Analysis of Quasilinear Inequalities on Complete Manifolds by Bruno Bianchini,Luciano Mari,Patrizia Pucci,Marco Rigoli Pdf

This book demonstrates the influence of geometry on the qualitative behaviour of solutions of quasilinear PDEs on Riemannian manifolds. Motivated by examples arising, among others, from the theory of submanifolds, the authors study classes of coercive elliptic differential inequalities on domains of a manifold M with very general nonlinearities depending on the variable x, on the solution u and on its gradient. The book highlights the mean curvature operator and its variants, and investigates the validity of strong maximum principles, compact support principles and Liouville type theorems. In particular, it identifies sharp thresholds involving curvatures or volume growth of geodesic balls in M to guarantee the above properties under appropriate Keller-Osserman type conditions, which are investigated in detail throughout the book, and discusses the geometric reasons behind the existence of such thresholds. Further, the book also provides a unified review of recent results in the literature, and creates a bridge with geometry by studying the validity of weak and strong maximum principles at infinity, in the spirit of Omori-Yau’s Hessian and Laplacian principles and subsequent improvements.

Author : Alexander A. Balinsky,W. Desmond Evans,Roger T. Lewis
Publisher : Springer
Page : 263 pages
File Size : 43,7 Mb
Release : 2015-10-20
Category : Mathematics
ISBN : 9783319228709

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The Analysis and Geometry of Hardy's Inequality by Alexander A. Balinsky,W. Desmond Evans,Roger T. Lewis Pdf

This volume presents advances that have been made over recent decades in areas of research featuring Hardy's inequality and related topics. The inequality and its extensions and refinements are not only of intrinsic interest but are indispensable tools in many areas of mathematics and mathematical physics. Hardy inequalities on domains have a substantial role and this necessitates a detailed investigation of significant geometric properties of a domain and its boundary. Other topics covered in this volume are Hardy- Sobolev-Maz’ya inequalities; inequalities of Hardy-type involving magnetic fields; Hardy, Sobolev and Cwikel-Lieb-Rosenbljum inequalities for Pauli operators; the Rellich inequality. The Analysis and Geometry of Hardy’s Inequality provides an up-to-date account of research in areas of contemporary interest and would be suitable for a graduate course in mathematics or physics. A good basic knowledge of real and complex analysis is a prerequisite.

Author : Oene Bottema
Publisher : Unknown
Page : 160 pages
File Size : 50,7 Mb
Release : 1969
Category : Inequalities (Mathematics).
ISBN : UCAL:B5008790

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Geometric Inequalities by Oene Bottema Pdf

Author : Zdravko Cvetkovski
Publisher : Springer Science & Business Media
Page : 439 pages
File Size : 44,6 Mb
Release : 2012-01-06
Category : Mathematics
ISBN : 9783642237928

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Inequalities by Zdravko Cvetkovski Pdf

This work is about inequalities which play an important role in mathematical Olympiads. It contains 175 solved problems in the form of exercises and, in addition, 310 solved problems. The book also covers the theoretical background of the most important theorems and techniques required for solving inequalities. It is written for all middle and high-school students, as well as for graduate and undergraduate students. School teachers and trainers for mathematical competitions will also gain benefit from this book.

Author : Gabriel-Eduard Vîlcu
Publisher : MDPI
Page : 208 pages
File Size : 43,7 Mb
Release : 2021-03-09
Category : Mathematics
ISBN : 9783036502984

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Inequalities in Geometry and Applications by Gabriel-Eduard Vîlcu Pdf

This book presents the recent developments in the field of geometric inequalities and their applications. The volume covers a vast range of topics, such as complex geometry, contact geometry, statistical manifolds, Riemannian submanifolds, optimization theory, topology of manifolds, log-concave functions, Obata differential equation, Chen invariants, Einstein spaces, warped products, solitons, isoperimetric problem, Erdös–Mordell inequality, Barrow’s inequality, Simpson inequality, Chen inequalities, and q-integral inequalities. By exposing new concepts, techniques and ideas, this book will certainly stimulate further research in the field.