macbeth
Reputation
997
Next privilege 1,000 Rep.
 Feb 13 comment How to find isothermal coordinates equivalent to circles in far limit? This is interesting, Bob, but can you explain more? I'm not quite sure what you mean by "symmetric about the z = 0 plane" -- do you mean the same as "transformation of the complex plane symmetric about the y-axis"? Feb 12 asked Self-intersection and generic point Feb 11 answered How to find isothermal coordinates equivalent to circles in far limit? Feb 4 comment Measurability of eigenelements $s \mapsto (\varphi_k(s), \lambda_k(s))$ of Laplace-Beltrami on $M_s$ Just checking -- are you aware of work (including various pathologies) on the corresponding question for linear operators in general? For example, in Kato, Perturbation Theory for Linear Operators. Nov 15 awarded Nice Question Sep 24 awarded Autobiographer Jul 2 awarded Curious 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.