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3 votes
0 answers
273 views

Principal eigenvalue of Laplacian under volume preserving mean curvature flow

Consider a compact uniformly convex n-dimensional hypersurface $M_0$ without boundary , which is smoothly imbedded in $\mathbb R^{n+1}$ , and suppose that $M_0$ is represented locally by some diffeomo …
Enhao Lan's user avatar
  • 165
1 vote
1 answer
133 views

Solvability of $u_t=\nabla_{u_\theta} u_\theta -\frac{1}{2}\nabla R +\frac{1}{2\tau}u_\theta...

I ask a question in math.stackexchange, but nobody answer it. So, I ask here. In Cao and Zhu's paper about Ricci flow, the $\mathcal{L}$-geodesic is defined as picture below.In fact, $\mathrm{Ric}(X …
Enhao Lan's user avatar
  • 165
1 vote
2 answers
484 views

Derivation of the volume preserving mean curvature flow

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Picture above is from Huisken, Gerhard, The volume preserv …
Enhao Lan's user avatar
  • 165