All Questions

Consider a compact, connected $n$ dimensional Riemmanian manifold $\mathcal{N}$ and its $m$ dimensional closed submanifold $\mathcal{M}$ (with the metric coming from from the one defined on $\mathcal{...

I recently read an elegant paper of Bobkov Bobkov, S.G., On concentration of measure on the cube, J. Math. Sci., New York 165, No. 1, 60-70 (2010); translation from Probl. Mat. Anal. 44, 55-64 (2010)....

Bear with me, I'm not a professional geometer. Recently, I've been studying Logarithmic Sobolev Inequalities (LSI) for probability distributions on manifolds (e.g as done in works of Bobkvo et al. ...

Let $\mathbf{M}$ be a submanifold of $\mathbb{R}^n$ with the induced Euclidean metric, and $\mbox{Ricc} \geq - \kappa , \kappa \geq 0$, as well as diameter bounded by $D$. What is the best known ...

Let $S^K$ be the unit sphere embedded in $R^{K+1}$. $v \in S^K$ is randomly chosen from a uniform distribution over $S^K$. $A \subseteq S^K$ is a $d$-dimensional sub-manifold ($d \leq K$). Think of ...

Introduction Let $\mathcal{M}$ be a compact $m$ - dimensional Riemmanian manifold with normalized measure $\mu$ (derived from the metric). It is know that in this setting we have concentration ...