Search Results

I'm finding myself a little confused about Koszul-Malgrange holomorphic structures in a certain context. Suppose $M$ is a complex manifold, $N$ is a smooth manifold with a smooth complex vector bundle …

Okay I thought about it a bit more, and here is what I can say in general. We can find a neighbourhood $U\subset N$ such that $V|_U$ splits diffeomorphically as $U\times \mathbb{C}^n$ and the section …

Let $\mathbb{D}$ be the unit disk in $\mathbb{C}$ with closure $\overline{\mathbb{D}}$, and let $\varphi:\partial \mathbb{D}\to \partial \mathbb{D}$ be any continuous homeomorphism. Let $\mu$ be a smo …

Let $(M,g)$ be a smooth oriented closed Riemannian manifold, $E\to M$ a smooth vector bundle, and $C^{k,\alpha}(E)$ the Banach space of sections of $E$ that are $k$-times differentiable (with respect …

Let $(M,g)$ be a smooth compact Riemannian manifold and dimension $2$, $\Gamma$ a smooth vector bundle over $M$, and suppose $L: W^{k,2}(\Gamma)\to W^{k-2,2}(\Gamma)$ is a second order strongly ellipt …