Results 71 to 80 of about 654,419 (234)

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, Steen Markvorsen, Matteo Raffaelli   +2 more
wiley   +1 more source

Affine inequalities for L p $L_{p}$ -mixed mean zonoids

Journal of Inequalities and Applications, 2016
In this paper, we introduce the L p $L_{p}$ -mixed mean zonoid of convex bodies K and L, and we prove some important properties for the L p $L_{p}$ -mixed mean zonoid, such as monotonicity, GL ( n ) $\operatorname{GL}(n)$ covariance, and so on.
Tongyi Ma, Yuanyuan Guo, Yibin Feng
doaj   +1 more source

Isoperimetric and Poincaré Inequalities on Non-Self-Similar Sierpiński Sponges: the Borderline Case

Analysis and Geometry in Metric Spaces, 2022
In this paper we construct a large family of examples of subsets of Euclidean space that support a 1-Poincaré inequality yet have empty interior. These examples are formed from an iterative process that involves removing well-behaved domains, or more ...
Eriksson-Bique Sylvester, Gong Jasun
doaj   +1 more source

Towards a unified theory of Sobolev inequalities

, 2014
We discuss our work on pointwise inequalities for the gradient which are connected with the isoperimetric profile associated to a given geometry. We show how they can be used to unify certain aspects of the theory of Sobolev inequalities.
A. Alvino, A. Cianchi, A. Ehrhard, A. Ehrhard, A. Fiorenza, A. Fiorenza, A. Fiorenza, A. Garsia, A.M. Garsia, A.M. Garsia, A.P. Calderón, B. Jawerth, B. Jawerth, C. Bennett, C. Bennett, C. Borell, C. Borell, D. Bakry, D.E. Edmunds, E. Milman, E. Milman, E. Milman, E. Milman, E. Milman, E. Milman, E. Pustylnik, F. Almgren, F. Barthe, F. Barthe, F. Barthe, F. Barthe, F.J. Pérez Lázaro, G. Pisier, G.D. Allen, G.E. Karadzhov, G.E. Karadzhov, H. Brezis, H. Triebel, J. Bastero, J. Bergh, J. Heinonen, J. Malý, J. Martin, J. Martin, J. Martin, J. Martin, J. Martin, J. Martin, J. Martin, J. Martín, J. Martín, J. Martín, J. Xiao, K. Hansson, L. Fontana, L. Gross, L. Pick, L. Saloff-Coste, L. Slavíková, L. Tartar, M. Cwikel, M. Cwikel, M. Griebel, M. Krbec, M. Krbec, M. Ledoux, M. Ledoux, M. Mastylo, M. Milman, M. Milman, N. Trudinger, R. O’Neil, S. Gallot, S. Kesavan, S.G. Bobkov, S.G. Bobkov, T. Coulhon, T. Coulhon, T. Coulhon, T. Iwaniec, W. Beckner, Z. Ditzian, Z. Ditzian, Z. Ditzian   +83 more
core   +1 more source

On the stability of some isoperimetric inequalities for the fundamental tones of free plates [PDF]

Journal of Spectral Theory, 2016
We provide a quantitative version of the isoperimetric inequality for the fundamental tone of a biharmonic Neumann problem. Such an inequality has been recently established by Chasman adapting Weinberger's argument for the corresponding second order ...
D. Buoso, D. Buoso, L. Chasman, Luigi Provenzano   +3 more
semanticscholar   +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

Isoperimetric Inequalities in Simplicial Complexes

, 2013
In graph theory there are intimate connections between the expansion properties of a graph and the spectrum of its Laplacian. In this paper we define a notion of combinatorial expansion for simplicial complexes of general dimension, and prove that ...
A. Duval, A. Gundert, A. Gundert, A. Lubotzky, A. Lubotzky, A. Lubotzky, A. Marcus, A. Nilli, A. Żuk, B. Eckmann, D. Dotterrer, D. Puder, D. W. Matula, F. Chung, F. R. K. Chung, H. Garland, I. Newman, J. Cheeger, J. Dodziuk, J. Fox, J. Friedman, J. Friedman, J. Friedman, J. Matoušsek, J. Pach, J. Steenbergen, M. Blum, N. Alon, N. Alon, N. Alon, N. Linial, O. Parzanchevski, Ori Parzanchevski, P. Buser, P. Erdős, P. Erdős, R. Aharoni, R. Beigel, R. I. Oliveira, R. M. Tanner, R. Meshulam, Ran J. Tessler, Ron Rosenthal, S. Hoory, S. Janson, T. Tao, W. Kook, Y. Bilu   +47 more
core   +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

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

Un nuovo approccio alle disuguaglianze isoperimetriche quantitative

Bruno Pini Mathematical Analysis Seminar, 2011
We introduce a new variational method for studying geometric and functional inequalities with quantitative terms. In the context of isoperimetric-type inequalities, this method (called Selection Principle) is based on a penalization technique combined ...
Gian Paolo Leonardi
doaj