Results 81 to 90 of about 654,419 (234)

Shape optimization for an elliptic operator with infinitely many positive and negative eigenvalues

Advances in Nonlinear Analysis, 2018
This paper deals with an eigenvalue problem possessing infinitely many positive and negative eigenvalues. Inequalities for the smallest positive and the largest negative eigenvalues, which have the same properties as the fundamental frequency, are ...
Bandle Catherine, Wagner Alfred
doaj   +1 more source

Isoperimetric inequalities in surround system and space science

Journal of Inequalities and Applications, 2016
By means of the algebraic, analysis, convex geometry, computer, and inequality theories we establish the following isoperimetric inequality in the centered 2-surround system S ( 2 ) { P , Γ , l } $S^{(2)} \{P,\varGamma ,l \}$ : ( 1 | Γ | ∮ Γ r ¯ P p ) 1 /
JiaJin Wen, Jun Yuan, ShanHe Wu
doaj   +1 more source

The Sine Transform of Isotropic Measures [PDF]

, 2012
Sharp isoperimetric inequalities for the sine transform of even isotropic measures are established. The corresponding reverse inequalities are obtained in an asymptotically optimal form.
Maresch, Gabriel, Schuster, Franz E.
core  

New Orlicz Affine Isoperimetric Inequalities

, 2014
The Orlicz-Brunn-Minkowski theory receives considerable attention recently, and many results in the $L_p$-Brunn-Minkowski theory have been extended to their Orlicz counterparts.
Ye, Deping
core   +1 more source

Quantitative magnetic isoperimetric inequality [PDF]

Journal of Spectral Theory
In 1996 Erdős showed that among planar domains of fixed area, the smallest principal eigenvalue of the Dirichlet Laplacian with a constant magnetic field is uniquely achieved on the disk. We establish a quantitative version of this inequality, with an explicit remainder term depending on the field strength that measures how much the domain deviates ...
Rohan Ghanta, Lukas Junge, Léo Morin
openaire   +3 more sources

Stability of reverse isoperimetric inequalities in the plane: Area, Cheeger, and inradius

Bulletin of the London Mathematical Society, Volume 58, Issue 2, February 2026.
Abstract In this paper, we present stability results for various reverse isoperimetric problems in R2$\mathbb {R}^2$. Specifically, we prove the stability of the reverse isoperimetric inequality for λ$\lambda$‐convex bodies — convex bodies with the property that each of their boundary points p$p$ supports a ball of radius 1/λ$1/\lambda$ so that the ...
Kostiantyn Drach, Kateryna Tatarko
wiley   +1 more source

Schur convex functions and the Bonnesen style isoperimetric inequalities for planar convex polygons

, 2018
In this note, we continue to investigate Bonnesen-type isoperimetric inequalities for planar convex polygons. We shall first establish some analytic isoperimetric inequalities for a special class of Schur convex functions.
Ji-bing Qi, W. Wang
semanticscholar   +1 more source

Pólya's conjecture for Dirichlet eigenvalues of annuli

Journal of the London Mathematical Society, Volume 113, Issue 2, February 2026.
Abstract We prove Pólya's conjecture for the eigenvalues of the Dirichlet Laplacian on annular domains. Our approach builds upon and extends the methods we previously developed for disks and balls. It combines variational bounds, estimates of Bessel phase functions, refined lattice point counting techniques and a rigorous computer‐assisted analysis. As
Nikolay Filonov, Michael Levitin, Iosif Polterovich, David A. Sher   +3 more
wiley   +1 more source

Flat currents modulo p in metric spaces and filling radius inequalities

, 2010
We adapt the theory of currents in metric spaces, as developed by the first-mentioned author in collaboration with B. Kirchheim, to currents with coefficients in Z_p. Building on S.
Ambrosio, Luigi, Katz, Mikhail G.
core   +1 more source

Counting Independent Sets in Percolated Graphs via the Ising Model

Random Structures &Algorithms, Volume 68, Issue 1, January 2026.
ABSTRACT Given a graph G$$ G $$, we form a random subgraph Gp$$ {G}_p $$ by including each edge of G$$ G $$ independently with probability p$$ p $$. We provide an asymptotic expansion of the expected number of independent sets in random subgraphs of regular bipartite graphs satisfying certain vertex‐isoperimetric properties, extending the work of ...
Anna Geisler, Mihyun Kang, Michail Sarantis, Ronen Wdowinski   +3 more
wiley   +1 more source