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bio website math.princeton.edu/~macbeth
location Princeton
age 27
visits member for 5 years
seen Dec 15 at 5:12

I'm a fifth-year graduate student in Princeton.


Nov
15
awarded  Nice Question
Sep
24
awarded  Autobiographer
Jul
2
awarded  Curious
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26
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15
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15
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22
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25
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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
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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