Glen Wheeler
Reputation
1,925
Next privilege 2,000 Rep.
Edit questions and answers
 Dec 2 awarded Yearling Jul 17 comment When does gradient flow not converge? Hi Anthony -- in my paper on generalised Helfrich flow of space curves I have a few examples of functionals that give rise to nonconvergence; I talk both about your groove possibility as well as some solutions of translation type. These are all gradient flows. (Unlike e.g. IMCF of a star-shaped hypersurface.) Jun 7 answered Problem involving divergence theorem and laplacian squared Jan 13 comment Proof of Wirtinger inequality This is not weaker. It does not require $f(b) = 0$. Dec 2 awarded Yearling Nov 19 awarded Taxonomist Sep 30 awarded Explainer Aug 17 awarded Necromancer Jul 28 awarded Nice Answer Jul 11 comment Soft question: How does basic differential geometry “fit together”? You're not looking for a book recommendation, you just want a high-level map? The problem is that there is no way to fit even just the names and connections between all topics in diff geom on one page. You're going to have to be more specific. Jul 2 awarded Curious Jun 17 awarded Notable Question Feb 10 awarded Good Answer Dec 2 awarded Yearling Oct 30 revised How solve this equation Tag incorrect Oct 30 suggested approved edit on How solve this equation Sep 27 awarded Popular Question Sep 10 comment How to solve this quasilinear parabolic evolution equation (result of curve shortening flow)? It is just a one dimensional quasilinear parabolic PDE... this is covered by standard theory. Can you explain more which texts you looked at? Did you check Lieberman for example? Sep 6 comment Geometric Interpretation: Parallel forms are harmonic See the answer for the first question. For the second: It isn't an arbitrary solution of the Laplacian, it's the Laplacian acting on the volume form. Sep 2 comment Geometric Interpretation: Parallel forms are harmonic The fact that the volume form is parallel implies that infinitesimal deformations of the volume form act exactly linearly. Since the Levi-Civita connection controls also the cotangent deformations, this implies that the volume form expands linearly in every possible direction. This is stronger than $\Delta \mu = 0$!