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Results tagged with geometric-analysis
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user 161514
3
votes
1
answer
265
views
A compact Riemann surface with a finite set of points removed is parabolic
A Riemann surface $\mathcal{R}$ is called parabolic if it is not compact and doesn't carry a negative non-constant subharmonic function, and is called hyperbolic if it carries a negative non-constant …
- 438
2
votes
1
answer
254
views
The space of Sobolev maps between Riemannian manifolds
Let $\mathcal{M}, \mathcal{N}$ be two Riemannian manifods. Suppose that $\mathcal{N}$ is properly and isometrically embedded in $\mathbb{R}^n$. The space of Sobolev maps between $\mathcal{M}$ and $\m …
- 438
7
votes
2
answers
351
views
What's the limit of a sequence of harmonic maps between manifolds?
Let ${M}, \, {N}$ be two Riemannian manifolds, and let $u_n: {M} \to {N}$ be a sequence of harmonic maps.
Question. Suppose that $u_n$ converges uniformly to a (necessarily continuous) function $u$. …
- 438