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Let $M$ be a smooth $n$-dimensional manifold and $N\subset M$ be a closed embedded submanifold of codimension at least $2$. Furthermore, let $\mu$ be a volume form on $M$. Question: Does there ...

Suppose $M$ is a compact smooth manifold and $V$ is a compact complex manifold. I want to show that the spaces $C^{k,\alpha}(M,V)$ and $W^{k,p}(M,V)$ (the latter for $kp>\dim M$) are complex ...

Let $X$ be a complex manifold and $\omega$ a Kahler form on $X$. A smooth function $\rho$ is called a potential of $\omega$ if $i\partial\bar\partial\rho=\omega$. By intuition, it seems that $\rho$ ...