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Results tagged with geometric-analysis
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user 86341
2
votes
0
answers
84
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Is Colding-Minicozzi entropy continuous w.r.t. $C^\infty$ convergenge?
For an hypersurface $\Sigma^n \subseteq \mathbb{R}^{n+1}$ the entropy introduced by Colding and Minicozzi (see their paper) is defined as
$$
\lambda(\Sigma) := \sup_{x_0 \in \mathbb{R}^{n+1} \\ t_0 …
- 823
5
votes
0
answers
305
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On Colding-Minicozzi limit lamination theorem
Colding and Minicozzi proved the following limit lamination theorem (see Theorem 8.26 in "A course in Minimal Surfaces" by Colding and Minicozzi for the complete statement)
THEOREM: Let $\Sigma_i \su …
- 823
5
votes
1
answer
144
views
Stable region of minimal hypersurfaces with finite Morse index
In this Inventiones Mathematicae paper, Fischer-Colbrie proved the following result (Proposition 1):
Proposition: Let $ M$ be a complete two-sided minimal surface in a three manifold $N$. Then if $M …
- 823