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Apr
21
accepted Can one smooth open star shaped domains from the inside by star shaped domains?
Apr
5
comment Defining smooth manifolds without homeomorphisms
In the book "Differential Geometry: Manifolds, Curves, and Surfaces" by Berger and Gostiaux, $C^p$ structures on $X$ are defined without referring to some fixed topology on $X$ (p. 54). However, this definition doesn't contains hausdorffness and second countability, they are added later once $X$ has been endowed with a canonical topology (p. 55). However, if I understand correctly it doesn't answer your question, you would like to get hausdorffness and second countability just by adding extra conditions on the charts, right ?
Apr
4
comment Douglass integral and harmonic maps
If I am not mistaken when the source space is 2D, the harmonic map equation is conformally invariant, so there must an error in your computation.
Apr
1
comment Douglass integral and harmonic maps
If the question you ask is "are minimizers of E harmonic maps ?" then answer is yes.
Apr
1
comment Douglass integral and harmonic maps
You want an explicit number ? Do you require $f$ to be equal to a specific parametrization of $\Gamma$ on the boundary of $U$ ?
Mar
30
revised Distance to the level sets of an almost linear function
formatting
Mar
30
revised Distance to the level sets of an almost linear function
Added some context, fixed some typos.
Mar
30
comment Applying Cheeger and Colding segment inequality
Anyway, I asked another question which came out while reading the same set of notes : here. If you have any ideas to share, feel free to do it !
Mar
30
comment Applying Cheeger and Colding segment inequality
I actually had come to the same conclusion, and forgot I asked the question. Thanks anyway.
Mar
30
accepted Applying Cheeger and Colding segment inequality
Mar
17
revised Distance to the level sets of an almost linear function
improved formatting, added some details on notations
Mar
17
revised Distance to the level sets of an almost linear function
edited tags
Mar
17
asked Distance to the level sets of an almost linear function
Mar
17
comment Estimating $\left(\Gamma\left(\frac{\alpha}{\sqrt n}\right)\right)^n$ for fixed $\alpha >0$ as a function of (large) $n$
Can the asymptotic expansion of $\Gamma$ near zero given here (en.wikipedia.org/wiki/Gamma_function#General) be of some help ?
Mar
17
revised Some manifold which is not totally geodesic in a compact manifold
added 199 characters in body
Mar
17
answered Some manifold which is not totally geodesic in a compact manifold
Mar
17
comment Some manifold which is not totally geodesic in a compact manifold
Just to be sure, you ask for your conditions to hold for every normal vector field $n$ ?
Mar
17
comment Some manifold which is not totally geodesic in a compact manifold
You mean the catenoid right ? and minimal (say for hyper surfaces for simplicity) is by definition that the trace of the Weingarten map $X\mapsto \nabla_X n$ vanishes, so a minimal surface will not satisfy $\langle\nabla_Xn,X\rangle=0$ for every $X$. If I understand correctly your condition is the vanishing of the Weingarten map (or second fundamental form for that matter form), which is equivalent to being totally geodesic.
Mar
17
comment Some manifold which is not totally geodesic in a compact manifold
Is $N$ an hypersurface ? And what is the counter example in $\mathbb{R}^3$ ?
Mar
11
asked Applying Cheeger and Colding segment inequality