Isoperimetric Inequalities for Two-dimensional Riemannian Manifolds PDF Download
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Author: Chuan-Chih Hsiung
Publisher:
ISBN:
Category : Geometry, Riemannian
Languages : en
Pages : 13
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Book Description
Author: Chuan-Chih Hsiung
Publisher:
ISBN:
Category : Geometry, Riemannian
Languages : en
Pages : 13
Get Book Here
Book Description
Author: Manuel Ritoré
Publisher: Springer Nature
ISBN: 3031379012
Category : Mathematics
Languages : en
Pages : 470
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Book Description
This work gives a coherent introduction to isoperimetric inequalities in Riemannian manifolds, featuring many of the results obtained during the last 25 years and discussing different techniques in the area. Written in a clear and appealing style, the book includes sufficient introductory material, making it also accessible to graduate students. It will be of interest to researchers working on geometric inequalities either from a geometric or analytic point of view, but also to those interested in applying the described techniques to their field.
Author: Isaac Chavel
Publisher: Cambridge University Press
ISBN: 9780521802673
Category : Mathematics
Languages : en
Pages : 292
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Book Description
This advanced introduction emphasizes the variety of ideas, techniques, and applications of the subject.
Author: Manuel Ritoré
Publisher: Springer Science & Business Media
ISBN: 3034602138
Category : Mathematics
Languages : en
Pages : 113
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Book Description
Geometric flows have many applications in physics and geometry. The mean curvature flow occurs in the description of the interface evolution in certain physical models. This is related to the property that such a flow is the gradient flow of the area functional and therefore appears naturally in problems where a surface energy is minimized. The mean curvature flow also has many geometric applications, in analogy with the Ricci flow of metrics on abstract riemannian manifolds. One can use this flow as a tool to obtain classification results for surfaces satisfying certain curvature conditions, as well as to construct minimal surfaces. Geometric flows, obtained from solutions of geometric parabolic equations, can be considered as an alternative tool to prove isoperimetric inequalities. On the other hand, isoperimetric inequalities can help in treating several aspects of convergence of these flows. Isoperimetric inequalities have many applications in other fields of geometry, like hyperbolic manifolds.
Author: Jürgen Rossmann
Publisher: Birkhäuser
ISBN: 3034886756
Category : Mathematics
Languages : en
Pages : 370
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Book Description
The contributions in this volume are dedicated to Vladimir G. Maz'ya and are par tially based on talks given at the conference "Functional Analysis, Partial Differ ential Equations, and Applications", which took place at the University of Rostock from August 31 to September 4, 1998, to honour Prof. Maz'ya. This conference (a satellite meeting of the ICM) gave an opportunity to many friends and colleagues from all over the world to honour him. This academic community is very large. The scientific field of Prof. Maz'ya is impressively broad, which is reflected in the variety of contributions included in the volumes. Vladimir Maz'ya is the author and co-author of many publications (see the list of publications at the end of this volume), the topics of which extend from functional analysis, function theory and numerical analysis to partial differential equations and their broad applications. Vladimir G. Maz'ya provided significant contributions, among others to the the ory of Sobolev spaces, the capacity theory, boundary integral methods, qualitative and asymptotic methods of analysis of linear and nonlinear elliptic differential equations, the Cauchy problem for elliptic and hyperbolic equations, the theory of multipliers in spaces of differentiable functions, maximum principles for elliptic and parabolic systems, and boundary value problems in domains with piecewise smooth boundaries. Surveys on Maz'ya's work in different fields of mathematics and areas, where he made essential contributions, form a major part of the present first volume of The Maz'ya Anniversary Collection.
Author: Gabriel-Eduard Vîlcu
Publisher: MDPI
ISBN: 303650298X
Category : Mathematics
Languages : en
Pages : 208
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Book Description
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.
Author: Yurii D. Burago
Publisher: Springer Science & Business Media
ISBN: 3662074419
Category : Mathematics
Languages : en
Pages : 346
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Book Description
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: Aleksandr Danilovich Aleksandrov
Publisher: American Mathematical Soc.
ISBN: 9780821818763
Category : Mathematics
Languages : en
Pages : 198
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Book Description
Proceedings and papers about in which the foundation of the intrinsic geometry of nonregular surfaces is developed.
Author: Chuan-Chih Hsiung
Publisher: World Scientific
ISBN: 9810243235
Category : Mathematics
Languages : en
Pages : 718
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Book Description
This invaluable book contains selected papers of Prof Chuan-Chih Hsiung, renowned mathematician in differential geometry and founder and editor-in-chief of a unique international journal in this field, the Journal of Differential Geometry.During the period of 1935-1943, Prof Hsiung was in China working on projective differential geometry under Prof Buchin Su. In 1946, he went to the United States, where he gradually shifted to global problems. Altogether Prof Hsiung has published about 100 research papers, from which he has selected 64 (in chronological order) for this volume.
Author: Mikhail Karpukhin
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
"Isoperimetric inequalities for eigenvalues of geometric operators have received a lot of attention in recent years. Such inequalities are of particular interest for the eigenvalues of Laplace and Dirichlet-to-Neumann operators on Riemannian manifolds, where they exhibit a surprising connection to the theory of minimal submanifolds. This bridge between analysis and geometry provides a path to solving problems from both fields. In the present manuscript we apply geometric methods to prove several new isoperimetric inequalities. In particular, we obtain an isoperimetric inequality for the first Laplace eigenvalue on non-orientable surfaces, improving upon results of P. Li and S.-T. Yau. We prove an isoperimetric inequality for all Steklov eigenvalues on orientable surfaces, improving upon results of A. Girouard and I. Polterovich. We also provide a high-dimensional analog of the latter inequality by considering Dirichlet-to-Neumann operators on differential forms. Finally, jointly with N. Nadirashvili, A. Penskoi and I. Polterovich we establish a sharp inequality for all Laplace eigenvalues on a two-dimensional sphere settling the conjecture of Nadirashvili proposed in 2002." --
