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Thursday, May 7, 2020 | History

6 edition of Isoperimetric Inequalities found in the catalog.

Isoperimetric Inequalities

Differential Geometric and Analytic Perspectives (Cambridge Tracts in Mathematics)

by Isaac Chavel

  • 96 Want to read
  • 25 Currently reading

Published by Cambridge University Press .
Written in English

    Subjects:
  • Calculus & mathematical analysis,
  • Geometry,
  • Topology,
  • Probability & Statistics - General,
  • Differential Geometry,
  • Mathematics,
  • Science/Mathematics,
  • Riemannian Manifolds,
  • General,
  • Geometry - Differential,
  • Mathematics / Differential Equations,
  • Geometry, Differential,
  • Isoperimetric inequalities

  • The Physical Object
    FormatHardcover
    Number of Pages280
    ID Numbers
    Open LibraryOL7754768M
    ISBN 100521802679
    ISBN 109780521802673

    We prove some old and new isoperimetric inequalities with the best constant using the ABP method applied to an appropriate linear Neumann problem. More precisely, we obtain a new family of sharp isoperimetric inequalities with weights (also called densities) in open convex cones of $\\mathbb{R}^n$. Our result applies to all nonnegative homogeneous weights satisfying a concavity condition in. The reader is referred to the book by Woess [63], which explores isoperimetric properties and random walks on in nite graphs. There is a close connection between discrete isoperimetric inequalities and their continuous counterpart, as evidenced in Section 7 to Size: KB.

      The purpose of this expository paper is to collect some (mainly recent) inequalities, conjectures, and open questions closely related to isoperimetric problems in real, finite-dimensional Banach spaces (= Minkowski spaces). We will also show that, in a way, Steiner symmetrization could be used as a useful tool to prove Petty's conjectured projection by: 4. An isoperimetric inequality on the discrete cube, and an elementary proof of the isoperimetric inequality in Gauss space Bobkov, S. G., The Annals of Probability, The Annals of Probability, Isoperimetric constants for product probability measures Bobkov, S. G. and Houdré, C.

    if its isoperimetric function is recursive [ECHLPT]. The main result in this paper is the following: Theorem The groups Aut(F n) and Out(F n) of automorphisms and outer automor-phisms of a flnitely generated free group F nsatisfy exponential isoperimetric inequalities, i.e. their isoperimetric functions are at most exponential. Yes, quite so. In fact it would be better to replace this so-called proof by (for instance) the proof from Hardy, Littlewood and Polya's book "Inequalities": they show that this isoperimetric inequality can be derived from Wirtinger's inequality (already proved in Wikipedia on its own page). Fathead99 , 11 June (UTC).


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Isoperimetric Inequalities by Isaac Chavel Download PDF EPUB FB2

The author discusses inequalities in Euclidean and Riemannian geometry, methods of classical differential geometry and elementary modern geometric measure, discretization of smooth spaces, and the influence of isoperimetric inequalities on heat diffusion on Riemannian ing only of a basic course in differential geometry, this Cited by: Isoperimetric Inequalities in Mathematical Physics.

(AM), Volume 27 (Annals of Mathematics Studies (27)) Paperback – Aug by G. Polya (Author), G. Szeg ö (Author) See all 2 formats and editions Hide other formats and editions. Price New from Author: G. Polya, G. Szegö.

12 rows  The description for this book, Isoperimetric Inequalities in Mathematical Physics. (AM). Isoperimetric inequality on the sphere: Among all smooth open subsets of ∂B 1 with given Isoperimetric Inequalities book N−1-measure a spherical cap (which is a set of the form ∂B 1 ∩ B ρ (P), for someρ > 0) has the smallest perimeter (= (N − 2)-boundary measure).

(3) Using the inequalities from Theorems – one can show isoperimetric inequalities for. The result is an introduction to the rich tapestry of ideas and techniques of isoperimetric inequalities, a subject that has its beginnings in classical antiquity and which continues to inspire Isoperimetric Inequalities book ideas in geometry and analysis to this very day--and beyond!Author: Isaac Chavel.

This book deals with the geometrical structure of finite dimensional normed spaces, as the dimension grows to infinity. This is a part of what came to be known as the Local Theory of Banach Spaces (this name was derived from the fact that in its first stages, this theory dealt mainly with relating the structure of infinite dimensional Banach spaces to the structure of their lattice of finite.

Isoperimetric inequalities and applications | Catherine Bandle | download | B–OK. Download books for free. Find books. The isoperimetric inequality (1) is valid also for a two-dimensional manifold of bounded curvature, which is a more general type of manifold than a Riemannian ty in (1) is attained for a non-regular object — a domain isometric to the lateral surface of a right circular cone with complete angle about the vertex.

Using (1), inequalities can be established for the length of a. These inequalities often arise as the final and most elaborate forms of previous, weaker (but already efficient) inequalities which will be mentioned in their framework throughout the book.

In these final forms however, the isoperimetric inequalities and associated concentration of measure phenomena provide the appropriate ideas for an in depth Author: Michel Ledoux, Michel Talagrand, Michel Talagrand.

Review of the hardback: 'The presentation of the book is clear and elegant, and gives expression to the beauty of the subject. It is a great pleasure to read this book, which is a profound source text for both classical and modern methods, and which will be equally valuable to graduate students and researchers in analysis 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 Mean Curvature Flow and Isoperimetric Inequalities *immediately available upon purchase as print book.

The description for this book, Isoperimetric Inequalities in Mathematical Physics. (AM), Vol will be forthcoming. Related Books Essential Discrete Mathematics for Computer Science Harry Lewis and Rachel Zax; The Fascinating World of Graph Theory. Free 2-day shipping. Buy Cambridge Tracts in Mathematics: Isoperimetric Inequalities (Hardcover) at In their famous book Isoperimetric Inequalities in Mathematical Physics, Pólya and Szegő extended this notion to include inequalities for domain functionals, provided that the equality sign is attained for some domain or in the limit as the domain degenerates [15].

2 Isoperimetric inequalities in “broader sense”File Size: KB. Additional Physical Format: Online version: Bandle, Catherine, Isoperimetric inequalities and applications.

Boston: Pitman, (OCoLC) 7 - Isoperimetric and universal inequalities for eigenvalues By Mark S. Ashbaugh, Department of Mathematics University of Missouri Columbia, MO e Cited by: The book description for the forthcoming "Isoperimetric Inequalities in Mathematical Physics.

(AM)" is not yet available. Most books on convexity also contain a discussion of the isoperimetric inequality from that perspective. One aspect of the subject is given by Burago [1].

Others may be found in a recent paper of the author [4] on Bonnesen inequalities and in the book of Santaló [4] on integral geometry and geometric probability. 2 The Isoperimetric Inequality 9 3. The curves c1(t) and c2(t) denote semi-circles Figure 2: Changing the Angle to Maximise the Area Again, look at Q1 and showed above that A1 = A2, therefore it is enough to show WLOG that c1(t) is a e c1(t) is not a The subsets on which the extremal values of I (or `) are attained are called isoperimetric subsets.

These problems are discrete analogies of some continuous problems, many of which can be found in the book of P'olya and Szego [99] devoted to continuous. Moreover, isoperimetric inequalities exist for polygons in two dimensions such as squares and VALIDATED CIRCULAR SHAPE SPACE 32 triangles (i.e.

the equilateral triangle is Author: Nicola Fusco.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 for nilpotent groups S. M. Gersten, D. F. Holt and T. R. Riley JanuRevised July 7, Appeared in Geom.

Funct. Analysis, 13, pagesAbstract We prove that every finitely generated nilpotent group of class c admits a polynomial isoperimetric function of degree c+1 and a linear.