Heat flow on 1-forms under lower Ricci bounds. Functional inequalities, spectral theory, and heat kernel

Mathias Braun

We study the canonical heat flow $({\mathsf{H}}_t{)}_{t\ge 0}$ on the cotangent module $L^2(T^{\ast }M)$ over an $\mathrm{RCD}(K,\infty )$ space $(M,\mathsf{d},\mathfrak{m})$, $K\in\boldsymb…