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Results tagged with geometric-analysis
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user 4572
5
votes
What's the limit of a sequence of harmonic maps between manifolds?
The answer to your question is no (i.e., if you do not impose any further assumptions). Consider the undoloidal Delaunay cylinder in $\mathbb R^3$, which come in a real 1-parameter family. These surfa …
- 6,825
6
votes
Accepted
A counterexample to a conjecture of Lawson
As already pointed out by Will Jagy there is an example in this paper by Karcher-Pinkall-Sterling. It is build from a tetrahedral tesselation of $S^3$ with dihedral angles $\tfrac{\pi}{2},$ $\tfrac{\p …
- 6,825
1
vote
Asymptotics of constant mean curvature surfaces
Note that it was asked in a previous version (before the question has been edited) for a heuristic argument for embedded ends to be asymptotically rotationally symmetric.
First of all, and similar to …
- 6,825
1
vote
Finding constant curvature metrics on surfaces for the case of positive Euler characteristic
One does not need the full Riemann-Roch theorem: It is enough to know the existence of a holomorphic map of degree $1$ to $CP^1$ for every compact Riemann surface $M$ of genus $0.$ There is the concep …
- 6,825