All Questions

In Yau and Schoen's differential geometry,in Ch5 before Thm 3.5,the author says When $R$(scalar curvature of a manifold M)$>0$,there exists a unique Green's function $G$ to the operator $L=-\Delta+...

Let $M = \mathbb{R}^3 \setminus B_1$ where $B_1$ is the unit ball (equip $M$ with the euclidean metric for simplicity, but it will be replaced by an arbitrary asymptotically flat metric). Let $N: L^2(\...

I've just read a review paper about Yau's conjecture on nodal sets of the eigenfunctions for the Laplace operator on manifolds. Briefly, if $\phi_\lambda$, $\lambda$ are an eigenpair for the Laplace-...

In this Inventiones Mathematicae paper, Fischer-Colbrie proved the following result (Proposition 1): Proposition: Let $ M$ be a complete two-sided minimal surface in a three manifold $N$. Then if $M$...

A smooth manifold $M$ is a manifold with a cylindrical end if there exists a compact subset $K\subset M$ such that $M\backslash K$ is diffeomorphic to $\Omega\times (r,\infty)$ where $\Omega$ is a ...

I am reading the paper"cohomology and Hodge theory on symplectic manifolds I" by Tseng and Yau. In this paper they consider several cohomologies on symplectic manifolds $(M,\omega)$based on the ...