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Results tagged with riemann-surfaces
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user 5659
Riemann surfaces(Riemannian surfaces) is one dimensional complex manifold. For questions about classical examples in complex analysis, complex geometry, surface topology.
6
votes
Hyperbolic Riemann Surface
Let $X'=X\setminus \overline {D(x,r_x)}$.
If $X$ is already hyperbolic, then the answer is yes (there is no entire curves in $X'$).
If $X=\mathbb C, \mathbb C^*$, then $X'$ has no entire curves by P …
- 2,727
2
votes
Subharmonic function on a twice punctured complex plane
A subharmonic function which is bounded from above near a polar set automatically extends through it.
Therefore, any negative subharmonic function on $\mathbb C \setminus\{0,1\}$ induces a negative s …
- 2,727
4
votes
Existence of a connection $A$ on a holomorphic line bundle $L$, s.t $F(A)=(\deg L)\omega$
Let $h_0$ be any hermitian metric on $L$, with curvature $F(h_0)$.
By Hodge theory, there exists a function $f\in \mathcal C^{\infty}(X)$ such that
$$\Delta_{\omega} f =\Lambda_{\omega} F(h_0) - \ma …
- 2,727
1
vote
Accepted
Stability of holomorphic vector bundles
For Question 1, let's take $E=E_1\oplus E_2$, and let $\mu$ be the slope of $E$ (which agrees with the slope of $E_1$ and $E_2$). Let $F\subset E$ be a subbundle and let $p:=\mathrm{pr_1}|_F:F\to E_1$ …
- 2,727