Gradient estimates for the heat semigroup on forms in a complete Riemannian manifold

Eric Amar

We study the heat equation $\frac{\partial u}{\partial t}-\Delta u=0,u(x,0)=\omega (x),$ where $\Delta :=d{d}^{\ast }+d^{\ast }d$ is the Hodge laplacian and $u(\cdot ,t)$ and $\omega$ are $p$-differential forms…