Results 11 to 20 of about 469,360 (206)
Notices of the American Mathematical SocietyThe isoperimetric problem is one of the oldest and most famous problems in geometry.
Eichmair, Michael, Brendle, Simon
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On the isoperimetric Riemannian Penrose inequality [PDF]
Communications on Pure and Applied MathematicsAbstractWe prove that the Riemannian Penrose inequality holds for asymptotically flat 3‐manifolds with nonnegative scalar curvature and connected horizon boundary, provided the optimal decay assumptions are met, which result in the mass being a well‐defined geometric invariant.
Benatti, Luca +2 more
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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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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 +10 more
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Isoperimetric Inequality for Disconnected Regions [PDF]
, 2021 The discrete isoperimetric inequality in Euclidean geometry states that among all $n$-gons having a fixed perimeter $p$, the one with the largest area is the regular $n$-gon.
Sanki, Bidyut, Vadnere, Arya
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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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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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