论文信息 - Manifolds with Density - 字舞流文

Manifolds with Density

Introduction We consider a Riemannian manifold M n with a positive density function Ψ (x) used to weight volume and hypersurface area. In terms of the underlying Riemannian volume dV 0 and area dA 0 , the new, weighted volume and area are given by

Frank Morgan | F. Morgan

[1] Hermann Karcher,et al. A general comparison theorem with applications to volume estimates for submanifolds , 1978 .

[2] J. Kuelbs. Probability on Banach spaces , 1978 .

[3] V. Sudakov,et al. Extremal properties of half-spaces for spherically invariant measures , 1978 .

[4] M. Wodzicki. Lecture Notes in Math , 1984 .

[5] F. Morgan. Regularity of isoperimetric hypersurfaces in Riemannian manifolds , 2003 .

[6] C. Borell. The Brunn-Minkowski inequality in Gauss space , 1975 .

[7] V. Milman,et al. Asymptotic Theory Of Finite Dimensional Normed Spaces , 1986 .

[8] F. Morgan. Geometric Measure Theory: A Beginner's Guide , 1988 .

[9] M. Gromov,et al. Isoperimetry of Waists and Concentration of Maps , 2003 .

[10] V. Bayle. Propriétés de concavité du profil isopérimétrique et applications , 2003 .

[11] N. Bingham. Probability Theory: An Analytic View , 2002 .

[12] F. Barthe. Extremal Properties of Central Half-Spaces for Product Measures , 2001 .

[13] Frank Morgan,et al. Some Sharp Isoperimetric Theorems for Riemannian Manifolds , 2000 .

[14] M. Ledoux,et al. Lévy–Gromov’s isoperimetric inequality for an infinite dimensional diffusion generator , 1996 .