All Questions

Let $M$ be a simply-connected $d$-dimensional Riemannian manifold with boundary (for simplicity assume a ball). Consider the boundary value problem for $\omega\in\Omega^k(M)$, $$ d\omega = \alpha \...

This is a bit of a followup to my previous question Intuition for the volume form - combinatorial definition?. I am looking for a certain combinatorial intuition when it comes to integrating ...

I have a seemingly basic question that I cannot find any literature on. Let $(M,g)$ be a smooth Riemannian manifold and let $\Delta:\Omega^1(M) \to \Omega^1(M)$ be the Laplace-De Rham operator on $1$-...

Let (M,g) be a complete Riemannian manifold. It is well known that the Laplace operator is essentially self-adjoint on $C^\infty_c(M)$. This extends to the (de Rahm) Laplace operator on forms. Thus in ...

This may be a simple question, but I decided to post it here (not just on MSE) because it is very related to a research topic: capillary surfaces. Let $(M^3,g)$ be a Riemannian $3$-manifold with ...