bio | website | |
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age | 26 | |
visits | member for | 4 years, 3 months |
seen | Mar 24 at 22:16 | |
stats | profile views | 1,946 |
I'm a fourth-year graduate student in Princeton.
Dec 26 |
awarded | Yearling |
Oct 15 |
awarded | Caucus |
Oct 15 |
awarded | Constituent |
Jul 22 |
awarded | Informed |
Jun 25 |
awarded | Citizen Patrol |
Jun 19 |
answered | Aubin's book - construction of Green's function on compact manifold |
Mar 7 |
awarded | Popular Question |
Feb 27 |
asked | “Mathai-Quillen-type” form on $M\times M$? |
Dec 26 |
awarded | Yearling |
Dec 8 |
awarded | Organizer |
Dec 7 |
revised |
Is the closure of the orbits of the mean curvature flow compact for a finite time?
edited tags |
Oct 18 |
comment |
Invariance group of Morse charts
(2.) Yes, we're interested in the diffeomorphisms satisfying $\varphi \circ f = \varphi$. Such a diffeo $f$ has the property that, on each level set $\{x:|x|^2=r\}$, $f$ restricts to a diffeo of the level set. Moreover the possible $f$ are basically characterized by this property. Think of $f$ as a (germ of a) 1-parameter family of diffeomorphisms of the $(n-1)$-sphere, modulo some boundary conditions (tending to the identity near 0) to ensure smoothness at $p$. |
Oct 18 |
comment |
Invariance group of Morse charts
Hi Will (and Kofi). (1.) It seems to me that one can work with the set of germs of charts near p, and the group of germs of diffeomorphisms fixing p. Then the action is well-defined and free and transitive. |
Sep 23 |
comment |
Dolbeault cohomology of Hopf manifolds
Very interesting and relevant. Thanks! |
Aug 28 |
comment |
Kahler manifolds with constant bisectional curvature
Regarding Walker's comment on Hawley's paper: The Bochner paper which is cited by Hawley is "Curvature in Hermitian metric" (1947). In this paper Bochner proves the local version of the result: that the metric of constant holomorphic bisectional curvature $b$ is unique up to local isometry. Maybe Walker felt that passing to the global version (as done by Hawley/Igusa) was straighforward. |
Jun 22 |
answered | Constant scalar curvature metrics in a conformal class |
Jun 2 |
awarded | Nice Question |
May 9 |
comment |
Finite groups admitting free isometric actions on round spheres
$\mathbb{Z}$ does act freely on $S^{2k+1}$ in the same way. This doesn't contradict Wolf's theorem -- the point is that this action is not properly discontinuous, so the quotient by this action is not a manifold. |
May 9 |
comment |
Finite groups admitting free isometric actions on round spheres
In your new answer, you're missing one group in the even-$n$ case: the group $\mathbb{Z}/2$, generated by the antipodal map $x\mapsto -x$. (Its eigenvalues are all $-1$, which is real.) |
May 9 |
comment |
Finite groups admitting free isometric actions on round spheres
This problem was solved by Joseph Wolf in his book "Spaces of Constant Curvature" (1967). (That is, if I understand the problem correctly -- so it's equivalent to the classification of complete manifolds of constant positive curvature.) I don't remember the answer -- its statement is quite involved |