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Results tagged with geometric-analysis
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user 125275
10
votes
Accepted
A better version of Weyl's Law or uniform estimates of Laplacian higher eigenvalues
It seems unlikely that such a bound holds except in very special cases. For instance, it fails for round spheres, which have very large multiplicity of eigenvalues. In fact, for spheres the eigenvalue …
- 6,001
5
votes
Which geometric variational problems admit an entropy identity?
In Kahler geometry, there is a long-standing open problem of determining which manifolds admit metrics of constant scalar curvature (cscK). In particular, there is a conjecture due to Yau, Tian and Do …
- 6,001
3
votes
Gradient of solution to heat equation under evolving metric
Let me expand a bit on my comment to try to answer your question.
In general, there is no relationship between the metrics $g(t)$ and the sub-bundle $V$, so it is possible to find examples where the g …
- 6,001
1
vote
Accepted
Neckpinch singularity of Ricci flow
It's not entirely clear what you mean by a local singularity, or what it might mean for a local singularity to be "global." I'll give one attempt to make those ideas precise. However, I won't be able …
- 6,001