Results 11 to 20 of about 1,599 (218)
Sobolev inequality and isoperimetric inequality for submanifolds in a smooth metric measure space
, 2023 Brendle recently proved a sharp Sobolev inequality and logarithmic Sobolev inequality for submanifolds in Euclidean space. From the sharp Sobolev inequality, he achieved a breakthrough in the conjecture of isoperimetric inequality for minimal ...
Ho, Pak-tung
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Generalized isoperimetric inequalities [PDF]
Journal of Mathematical Physics, 1973 New inequalities for certain Green's functions are given. They may be interpreted physically in many ways, for example, as applying to the quantum mechanical motion of a particle in a potential or to diffusion in the presence of absorbers. These inequalities involve a symmetrization process very closely related to Steiner symmetrization used in the ...
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A sharp reverse Bonnesen-style inequality and generalization
Journal of Inequalities and Applications, 2019 We investigate the isoperimetric deficit of the oval domain in the Euclidean plane. Via the kinematic formulae of Poincaré and Blaschke, and Blaschke’s rolling theorem, we obtain a sharp reverse Bonnesen-style inequality for a plane oval domain, which ...
Pengfu Wang
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Dilation Type Inequalities for Strongly-Convex Sets in Weighted Riemannian Manifolds
Analysis and Geometry in Metric Spaces, 2021 In this paper, we consider a dilation type inequality on a weighted Riemannian manifold, which is classically known as Borell’s lemma in high-dimensional convex geometry.
Tsuji Hiroshi
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The Bonenblust-Hille inequality for homogeneous polynomials is hypercontractive [PDF]
, 2011 The Bohnenblust-Hille inequality says that the $\ell^{\frac{2m}{m+1}}$ -norm of the coefficients of an $m$-homogeneous polynomial $P$ on $\Bbb{C}^n$ is bounded by $\| P \|_\infty$ times a constant independent of $n$, where $\|\cdot \|_\infty$ denotes the
Defant, Andreas +9 more
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Thermodynamic instabilities of generalized exotic BTZ black holes
Journal of High Energy Physics, 2019 We examine the conjecture that black holes violating the reverse isoperimetric inequality have negative specific heat at constant volume C V [1]. We test this conjecture on the family of generalized exotic Bañados, Teitelboim and Zanelli (BTZ) black ...
Wan Cong, Robert B. Mann
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Relative Isoperimetric Inequality for Minimal Submanifolds in a Riemannian Manifold
Journal of Inequalities and Applications, 2010 Let Σ be a domain on an m-dimensional minimal submanifold in the outside of a convex set C in 𝕊n or ℍn. The modified volume M(Σ) is introduced by Choe and Gulliver (1992) and we prove a sharp modified relative isoperimetric
Juncheol Pyo
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Isoperimetric inequalities in nonlocal diffusion problems with integrable kernel [PDF]
Opuscula MathematicaWe deduce isoperimetric estimates for solutions of linear stationary and evolution problems. Our main result establishes the comparison in norm between the solution of a problem and its symmetric version when nonlocal diffusion defined through integrable
Gonzalo Galiano
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On singular quasilinear elliptic equations with data measures
Advances in Nonlinear Analysis, 2021 The aim of this work is to study a quasilinear elliptic equation with singular nonlinearity and data measure. Existence and non-existence results are obtained under necessary or sufficient conditions on the data, where the main ingredient is the ...
Alaa Nour Eddine +2 more
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Randomized Isoperimetric Inequalities [PDF]
, 2017 We discuss isoperimetric inequalities for convex sets. These include the classical isoperimetric inequality and that of Brunn-Minkowski, Blaschke-Santalo, Busemann-Petty and their various extensions. We show that many such inequalities admit stronger randomized forms in the following sense: for natural families of associated random convex sets one has ...
Paouris, Grigoris, Pivovarov, Peter
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