Kei Funano

Concentration of 1-Lipschitz maps into an infinite dimensional l^p-ball with the l^q -distance function

In this paper, we study the Levy-Milman concentration phenomenon of 1-Lipschitz maps into infinite dimensional metric spaces. Our main theorem asserts that the concentration to an infinite dimensional l p -ball with the l q -distance function for 1 ≤ p < q ≤ +∞ is equivalent to the concentration to the real line.

Macroscopic scalar curvature and areas of cycles

In this paper we prove the following. Let

Concentration, Ricci Curvature, and Eigenvalues of Laplacian

{\Sigma}

Estimates of Gromov’s box distance

Σ be an n–dimensional closed hyperbolic manifold and let g be a Riemannian metric on

L^{p}

{\Sigma \times \mathbb{S}^1}

\mbi{R}

Σ×S1. Given an upper bound on the volumes of unit balls in the Riemannian universal cover