共查询到20条相似文献,搜索用时 343 毫秒
1.
Bernd Su˙ssmann 《Annals of Global Analysis and Geometry》2006,29(4):323-332
In this paper the classical Banchoff–Pohl inequality, an isoperimetric inequality for nonsimple closed curves in the Euclidean plane, involving the square of the winding number, is generalized to symmetric Minkowski geometries. The proof uses the well-known curve shortening flow. 相似文献
2.
We prove a sharp isoperimetric inequality in the Grushin plane and compute the corresponding isoperimetric sets. 相似文献
3.
Gil Solanes 《Differential Geometry and its Applications》2011,29(5):653-659
We generalize Banchoff–Pohl?s isoperimetric inequality to complex affine space. 相似文献
4.
Ulrich Clarenz Heiko von der Mosel 《Calculus of Variations and Partial Differential Equations》2001,12(1):85-107
We consider parametric variational double integrals with elliptic Lagrangians F depending on the surface normal and prove a compactness theorem for -critical immersions. As a key ingredient for the relevant a priori estimates we use F. Sauvigny's F-conformal parameters adapted to the parametric integrand F. As a by-product of our analysis we obtain an isoperimetric inequality for -critical immersions generalizing the classical isoperimetric inequality for minimal surfaces.
Received November 19, 1999 / Accepted February 4, 2000 / Published online July 20, 2000 相似文献
5.
We prove a sharp upper bound and a lower bound for the first nonzero eigenvalue of the Wentzell–Laplace operator on compact manifolds with boundary and an isoperimetric inequality for the same eigenvalue in the case where the manifold is a bounded domain in a Euclidean space. We study some fourth order Steklov problems and obtain isoperimetric upper bound for the first eigenvalue of them. We also find all the eigenvalues and eigenfunctions for two kind of fourth order Steklov problems on a Euclidean ball. 相似文献
6.
Jie Xiao 《Advances in Mathematics》2007,211(2):417-435
This paper shows that each of the sharp (endpoint) Sobolev inequality and the isoperimetric inequality can be split into two sharp and stronger inequalities through either the 1-variational capacity or the 1-integral affine surface area. Furthermore, some related sharp analytic and geometric inequalities are also explored. 相似文献
7.
For embedded closed curves with curvature bounded below, we prove an isoperimetric inequality estimating the minimal area bounded by such curves for a fixed perimeter. 相似文献
8.
Xiang Gao 《Results in Mathematics》2011,59(1-2):83-90
In this paper, we derive an improved sharp version of a reverse isoperimetric inequality for convex planar curves of Pan and Zhang (Beitr?ge Algebra Geom 48:303?C308, 2007), with a simpler Fourier series proof. Moreover our result also confirm a conjecture by Pan et?al. (J Math Inequal (preprint), 2010). Furthermore we also present a stability property of our reverse isoperimetric inequality (near equality implies curve nearly circular). 相似文献
9.
P. R. Goodey 《Israel Journal of Mathematics》1982,42(1-2):132-150
This paper is concerned with establishing lower bounds for the integrals of the square of the lengths of area and perimeter
bisecting chords of planar convex sets. The results obtained provide verification of two recent conjectures of Lutwak. When
combined with the known upper bounds for these integrals they yield the classical isoperimetric inequality. The main proof
technique involves estimation of the winding numbers of the locus of the midpoints of the chords concerned. 相似文献
10.
We establish, by simple semigroup arguments, a Lévy-Gromov isoperimetric inequality for the invariant measure of an infinite dimensional diffusion generator of positive curvature with isoperimetric model the Gaussian measure. This produces in particular a new proof of the Gaussian, isoperimetric inequality. This isoperimetric inequality strengthens the classical logarithmic Sobolev inequality in this context. A local version for the heat kernel measures is also proved, which may then be extended into an isoperimetric inequality for the Wiener measure on the paths of a Riemannian manifold with bounded Ricci curvature.Oblatum 19-VI-1995 相似文献
11.
We establish, by simple semigroup arguments, a Lévy–Gromov isoperimetric inequality for the invariant measure of an infinite
dimensional diffusion generator of positive curvature with isoperimetric model the Gaussian measure. This produces in particular
a new proof of the Gaussian isoperimetric inequality. This isoperimetric inequality strengthens the classical logarithmic
Sobolev inequality in this context. A local version for the heat kernel measures is also proved, which may then be extended
into an isoperimetric inequality for the Wiener measure on the paths of a Riemannian manifold with bounded Ricci curvature.
Oblatum 19-VI-1995 相似文献
12.
主要研究几何体的Bonnesen型等周不等式.得到了两个关于四面体的Bonnesen型等周不等式;进一步地,给出了关于四面体的等周不等式的一个简单证明. 相似文献
13.
Xin-Min Zhang 《Journal of Geometry》1997,60(1-2):188-201
In this paper, we establish some Bonnesen-style isoperimetric inequalities for plane polygons via an analytic isoperimetric inequality and an isoperimetric inequality in pseudo-perimeters of polygons.1991 Mathematics Subject Classification 51M10, 51M25,52A40,26D10. 相似文献
14.
Jeffrey Streets 《Advances in Mathematics》2010,223(2):454-3542
We study the behavior of the Ricci Yang-Mills flow for U(1) bundles on surfaces. By exploiting a coupling of the Liouville and Yang-Mills energies we show that existence for the flow reduces to a bound on the isoperimetric constant or the L4 norm of the bundle curvature. We furthermore completely describe the behavior of long time solutions of this flow on surfaces. Finally, in Appendix A we classify all gradient solitons of this flow on surfaces. 相似文献
15.
A purely analytic proof is given for an inequality that has as a direct consequence the two most important affine isoperimetric
inequalities of plane convex geometry: The Blaschke-Santaló inequality and the affine isoperimetric inequality of affine differential
geometry. 相似文献
16.
O.S Rothaus 《Journal of Functional Analysis》1985,64(2):296-313
There is a simple equivalence between isoperimetric inequalities in Riemannian manifolds and certain analytic inequalities on the same manifold, more extensive than the familiar equivalence of the classical isoperimetric inequality in Euclidean space and the associated Sobolev inequality. By an isoperimetric inequality in this connection we mean any inequality involving the Riemannian volume and Riemannian surface measure of a subset α and its boundary, respectively. We exploit the equivalence to give log-Sobolev inequalities for Riemannian manifolds. Some applications to Schrödinger equations are also given. 相似文献
17.
Recently Frank and Seiringer have shown an isoperimetric inequality for nonlocal perimeter functionals arising from Sobolev seminorms of fractional order. This isoperimetric inequality is improved here in a quantitative form. 相似文献
18.
A sharp quantitative version of the anisotropic isoperimetric inequality is established, corresponding to a stability estimate
for the Wulff shape of a given surface tension energy. This is achieved by exploiting mass transportation theory, especially
Gromov’s proof of the isoperimetric inequality and the Brenier-McCann Theorem. A sharp quantitative version of the Brunn-Minkowski
inequality for convex sets is proved as a corollary. 相似文献
19.
Erwin Lutwak 《Israel Journal of Mathematics》1977,28(3):249-253
The mixed width-integrals are defined and shown to have properties similar to those of the mixed volumes of Minkowski. An
inequality is established for the mixed width-integrals analogous to the Fenchel-Aleksandrov inequality for the mixed volumes.
An isoperimetric inequality (involving the mixed width-integrals) is presented which generalizes an inequality recently obtained
by Chakerian and Heil. Strengthened versions of this general inequality are obtained by introducing indexed mixed width-integrals.
This leads to an isoperimetric inequality similar to Busemann’s inequality involving concurrent cross-sections of convex bodies. 相似文献
20.
Xavier CABR''E 《数学年刊B辑(英文版)》2017,38(1):201-214
This paper presents the proof of several inequalities by using the technique introduced by Alexandroff, Bakelman, and Pucci to establish their ABP estimate. First, the author gives a new and simple proof of a lower bound of Berestycki, Nirenberg, and Varadhan concerning the principal eigenvalue of an elliptic operator with bounded measurable coefficients. The rest of the paper is a survey on the proofs of several isoperimetric and Sobolev inequalities using the ABP technique. This includes new proofs of the classical isoperimetric inequality, the Wulff isoperimetric inequality, and the Lions-Pacella isoperimetric inequality in convex cones. For this last inequality, the new proof was recently found by the author, Xavier Ros-Oton, and Joaquim Serra in a work where new Sobolev inequalities with weights came up by studying an open question raised by Haim Brezis. 相似文献