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Results tagged with cv.complex-variables
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user 36974
Complex analysis, holomorphic functions, automorphic group actions and forms, pseudoconvexity, complex geometry, analytic spaces, analytic sheaves.
4
votes
2
answers
517
views
A question about complex Laplacian on compact Hermitian manifolds
Let $(M,g)$ be a complex $n$-dim compact connected Hermitian manifold, and $\Delta_c(\cdot):=g^{i\bar{j}}\partial_i\partial_{\bar{j}}(\cdot)$ the complex Laplacian acting on smooth functions on $M$. …
- 593
1
vote
1
answer
143
views
Upper bound of the dimension of automorphism group of compact Kähler manifolds
It is well-known that the dimension of the isometry group of an $n$-dimensional compact Riemannian manifold is no larger than $\frac{1}{2}n(n+1)$, which is attained precisely by $S^n$ and $\mathbb{R}P …
- 593
1
vote
1
answer
94
views
a question about complex Hessians on complex tori
Suppose we have a real-valued smooth function on a complex torus:
$$f: \mathbb{C}^n/(\mathbb{Z}+\sqrt{-1}\mathbb{Z})^n\longrightarrow\mathbb{R},$$
i.e., this $f$ is a real-valued smooth function on $ …
- 593