Moment estimates, exponential integrability, concentration inequalities and exit times estimates on evolving manifolds

Abstract

On a smooth (not necessarily compact) manifold $M$ equipped with a ${\mathsf{C}}^1$-family of complete Riemannian metrics $g(t)$ and a ${\mathsf{C}}^{1,\infty }$-family of vector fields $Z(t)$ both indexed by the real interval $[0,T)$ where $T\in (0,\infty ]$, we prove moment estimates, exponential integrability, concentration inequalities and exit times estimates for diffusions on complete evolving Riemannian manifolds.