Results 191 to 200 of about 654,419 (234)

Several isoperimetric inequalities of Dirichlet and Neumann eigenvalues of the Witten Laplacian

Journal of Spectral Theory
In this paper, by mainly using the rearrangement technique and suitably constructing trial functions, under the constraint of fixed weighted volume, we successfully obtain several isoperimetric inequalities for the first and the second Dirichlet ...
Ruifeng Chen, Jing Mao
semanticscholar   +1 more source

Isoperimetric Inequalities in Riemann Surfaces and Graphs

Journal of Geometric Analysis, 2018
A celebrated theorem of Kanai states that quasi-isometries preserve isoperimetric inequalities between uniform Riemannian manifolds (with positive injectivity radius) and graphs.
Álvaro Martínez-Pérez, José M. Rodríguez   +1 more
semanticscholar   +1 more source

ISOPERIMETRIC INEQUALITIES FOR MULTIVARIFOLDS

Mathematics of the USSR-Izvestiya, 1986
Developing the theory of multivarifolds the author establishes new isoperimetric inequalities. The main result can be stated as follows: ''Let W be a \((k+1)\)-dimensional compact Riemannian manifold with boundary \(\partial W\), and \(g: \partial W\to R^ n\) a fixed mapping of class \(C^ r\) (resp. a locally Lipschitz mapping).
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Isoperimetric Inequalities and Eigenvalues

SIAM Journal on Discrete Mathematics, 1997
Summary: An upper bound is given on the minimum distance between \(i\) subsets of same size of a regular graph in terms of the \(i\)th largest eigenvalue in absolute value. This yields a bound on the diameter in terms of the \(i\)th largest eigenvalue for any integer \(i\). Our bounds are shown to be asymptotically tight for explicit families of graphs
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Generalized isoperimetric inequalities. III

Journal of Mathematical Physics, 1973
The generalized isoperimetric inequalities for rearranged Green's functions, which have previously been discussed for a rearrangement process analogous to Steiner symmetrization, are obtained for a type of rearrangement analogous to circular symmetrization.
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Isoperimetric Inequalities in Riemannian Manifolds

PROGRESS IN MATHEMATICS, 2023
M. Ritoré
semanticscholar   +1 more source

Relative isoperimetric inequality and¶linear isoperimetric inequality for minimal submanifolds

manuscripta mathematica, 1998
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Isoperimetric Inequalities for Soluble Groups

Geometriae Dedicata, 2001
A theorem of D. F. Holt states that a nilpotent group is automatic if and only if it is virtually Abelian (Theorem 8.2.8 of [\textit{D. B. A. Epstein} et al., Word processing in groups, Jones and Bartlett, Boston (1992; Zbl 0764.20017)]). In the paper under review, the authors investigate the question of whether this theorem still holds if nilpotent ...
Groves, J. R. J., Hermiller, S. M.
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The Isoperimetric inequality

Resonance, 2002
A new proof (due to X Cabre) of the classical isoperimetric theorem, based on Alexandrov’s idea of moving planes, will be presented. Compared to the usual proofs, which use geometric measure theory, this proof will be based on elementary ideas from calculus and partial differential equations (Laplace equation).
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Spherical isoperimetric inequalities

2019
This thesis contains contributions to the theory of convex bodies, that is, convex, compact sets, in spaces of constant curvature, in particular, the Euclidean unit sphere. First, a definition of centroid bodies on the sphere is given by mimicking the geometric construction from flat space.
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