3 problems

Braverman–Milatovic–Shubin conjecture. If $(M,g)$ is a geodesically complete Riemannian manifold, then the $L^2$-positivity preserving property holds.

Let $(V,E)$ be a graph, choose a fixed root $x^*\in V$, and let $B_r$ be the ball of radius $r$ about $x^*$. Let $\partial B_r$ denote its outer vertex boundary, and write $\#A$ fo…

A complete noncompact Riemannian manifold is stochastically incomplete if its heat kernel $p(x,y,t)$ satisfies … for some, equivalently any, $(x,t)\in M\times(0,+\infty)$; otherwis…