Results 61 to 70 of about 469,360 (206)
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 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 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
Isoperimetric inequality in the Grushin plane [PDF]
, 2018 We prove a sharp isoperimetric inequality in the Grushin plane and compute the corresponding isoperimetric ...
Morbidelli, Daniele, Monti, Roberto
core
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
Reverse isoperimetric inequalities for Lagrangian intersection Floer theory
Bulletin of the London Mathematical Society, Volume 58, Issue 2, February 2026.Abstract We extend Groman and Solomon's reverse isoperimetric inequality to pseudoholomorphic curves with punctures at the boundary and whose boundary components lie in a collection of Lagrangian submanifolds with intersections locally modelled on Rn∩(Rk×−1Rn−k)$\mathbb {R}^n\cap (\mathbb {R}^{k}\times \sqrt {-1}\mathbb {R}^{n-k})$ inside Cn$\mathbb {C}
J. ‐P. Chassé, J. Hicks, Y. J. Nho
wiley +1 more source
Super-entropic black holes in gravity’s rainbow and determining constraints on rainbow functions
European Physical Journal C: Particles and FieldsThis paper is motivated by the application of the inverse isoperimetric inequality to establish constraints on the parameters of gravity’s rainbow. We investigate the thermodynamic (in)stability conditions for d-dimensional energy-dependent black holes ...
Behzad Eslam Panah +3 more
doaj +1 more source
Advanced Nonlinear Studies, 2021 Through conformal map, isoperimetric inequalities are equivalent to the Hardy–Littlewood–Sobolev (HLS) inequalities involved with the Poisson-type kernel on the upper half space.
Tao Chunxia
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Stability of reverse isoperimetric inequalities in the plane: Area, Cheeger, and inradius
Bulletin of the London Mathematical Society, Volume 58, Issue 2, February 2026.Abstract In this paper, we present stability results for various reverse isoperimetric problems in R2$\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
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 +3 more
wiley +1 more source