Results 61 to 70 of about 520,398 (211)
Semiclassical inequalities for Dirichlet and Neumann Laplacians on convex domains
Communications on Pure and Applied Mathematics, Volume 79, Issue 3, Page 762-822, March 2026.Abstract We are interested in inequalities that bound the Riesz means of the eigenvalues of the Dirichlet and Neumann Laplacians in terms of their semiclassical counterpart. We show that the classical inequalities of Berezin–Li–Yau and Kröger, valid for Riesz exponents γ≥1$\gamma \ge 1$, extend to certain values γ<1$\gamma <1$, provided the underlying ...
Rupert L. Frank, Simon Larson
wiley +1 more source
Isoperimetric Inequalities for Convex Cones [PDF]
Proceedings of the American Mathematical Society, 1990 We present here an isoperimetric inequality for sets contained in a convex cone. Some applications to symmetrization problems and Sobolev inequalities are also indicated.
LIONS P. L., PACELLA, Filomena
openaire +3 more sources
On the quantitative isoperimetric inequality in the plane [PDF]
, 2017 International audienceIn this paper we study the quantitative isoperimetric inequality in the plane. We prove the existence of a set $\Omega$, different from a ball, which minimizes the ratio $\delta(\Omega)/\lambda^2(\Omega)$, where $\delta$ is the ...
Chiara Bianchini +5 more
core +1 more source
The isoperimetric inequality in Rⁿ
, 2011 This thesis presents a complete proof of the isoperimetric inequality for a smooth surface in Euclidean space. The proof uses the Brunn-Minkowski Inequality, the formulae for the first variations of area and Alexandrov’s theorem.Science, Faculty ...
Ross, Carol
core +1 more source
The convex hull of a convex space curve with four vertices
Bulletin of the London Mathematical Society, Volume 58, Issue 3, March 2026.Abstract We obtain an upper bound for the volume of the convex hull of a simple closed Frenet curve with exactly four vertices, that is, four points of vanishing torsion, and lying on the boundary of its convex hull. Moreover, we show that the upper bound is attained when the curve intersects every plane in at most four points, a condition studied by ...
Jakob Bohr +2 more
wiley +1 more source
Isoperimetric inequalities in graphs and surfaces [PDF]
Electronic Notes in Discrete Mathematics, 2014 Abstract Let M be the set of metric spaces that are either graphs with bounded degree or Riemannian manifolds with bounded geometry. Kanai proved the quasi-isometric stability of several geometric properties (in particular, of isoperimetric inequalities) for the spaces in M .
Cantón Pire, Alicia +3 more
openaire +3 more sources
Quantitative stability in the isodiametric inequality via the isoperimetric inequality
, 2014 The isodiametric inequality is derived from the isoperimetric inequality through a variational principle, establishing that balls maximize the perimeter among convex sets with fixed diameter.
Ponsiglione M. +7 more
core +2 more sources
Exact bounds for tail probabilities of martingales with bounded differences
Lietuvos Matematikos Rinkinys, 2009 We consider random walks, say Wn = {0, M1, . . ., Mn} of length n starting at 0 and based on a martingale sequence Mk = X1 + ··· + Xk with differences Xm. Assuming |Xk| \leq 1 we solve the isoperimetric problem Bn(x) = supP\{Wn visits an interval [x,∞
Dainius Dzindzalieta
doaj +1 more source
Isoperimetric inequalities of the fourth order Neumann eigenvalues
Journal of Inequalities and Applications, 2020 In this paper, we obtain some isoperimetric inequalities for the first ( n − 1 ) $(n-1)$ eigenvalues of the fourth order Neumann Laplacian on bounded domains in an n-dimensional Euclidean space. Our result supports strongly the conjecture of Chasman.
Yanlin Deng, Feng Du
doaj +1 more source
Harmonic maps to the circle with higher dimensional singular set
Proceedings of the London Mathematical Society, Volume 132, Issue 3, March 2026.Abstract In a closed, oriented ambient manifold (Mn,g)$(M^n,g)$ we consider the problem of finding S1$\mathbb {S}^1$‐valued harmonic maps with prescribed singular set. We show that the boundary of any oriented (n−1)$(n-1)$‐submanifold can be realised as the singular set of an S1$\mathbb {S}^1$‐valued map, which is classically harmonic away from the ...
Marco Badran
wiley +1 more source