bio | website | perso-math.univ-mlv.fr/users/… |
---|---|---|
location | Créteil | |
age | 30 | |
visits | member for | 4 years, 7 months |
seen | 2 hours ago | |
stats | profile views | 1,369 |
Now at "Université Paris Est Créteil". I work in Riemannian geometry, and more specifically on Ricci flow.
Mar 22 |
comment |
A version of isotone projection cones
What about the projection from $\mathbb{R}^2$ to $C=\{y=-x\}$, with $a=(0,2)$ and $b=(0,0)$ ? It seems to prove that the general statement you were looking for is false. |
Feb 26 |
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Obstruction to the existence of global isometries on a constant-curvature Riemannian manifold
Even in the case where $M$ is simply-connected $(M,g)$ need not be an open subset of a complete constant curvature manifold: consider for instance the universal cover of an open subset of the plane with several holes. |
Feb 23 |
comment |
Existence and uniqueness of a quasi-linear pde system on a surface
May I inquire where this equation come from ? Can it be written in a more geometric fashion ? Does it encode some special properties of the 1-form $I_\alpha dx^\alpha$ ? If you manage to present your question in this way, this would help us giving you more precise answers. |
Dec 9 |
comment |
Surjectivity of “nice maps” from local properties
For your example from analysis, don't you need to assume that your map $f$ is proper ? It seems to me that the inclusion map from an open subset of $\mathbb{R}^d$ to $\mathbb{R}^d$ is a counterexample. |
Dec 3 |
revised |
Frobenius Condition for a specific first order pde
added 104 characters in body |
Dec 3 |
comment |
Frobenius Condition for a specific first order pde
My bad. This case is integrable actually. |
Dec 2 |
revised |
metric on ${\bf SPD}_n({\mathbb R})$
added 36 characters in body |
Dec 2 |
answered | metric on ${\bf SPD}_n({\mathbb R})$ |
Dec 2 |
revised |
Frobenius Condition for a specific first order pde
Added the fact that the solution needs to be non constant. |
Dec 2 |
comment |
Frobenius Condition for a specific first order pde
Ok, I did the computation: if $u$ solves the problem, so does any $f(u)$ for $f$ a smooth function from $\mathbb{R}$ to $\mathbb{R}$. So I'll take $u(x,y,z)=z^2-y^2$ instead of yours. Then $\nabla\phi_1=\partial_x$ and $\nabla\phi_2=yz\partial_x+xz\partial_y+xy\partial_z$, while $\nabla u= 2z\partial_z-2y\partial_y$. On can check that the inner products between the gradients don't vanish everywhere. |
Nov 29 |
comment |
Frobenius Condition for a specific first order pde
I'll have a look but I'm skeptical. |
Nov 28 |
answered | Frobenius Condition for a specific first order pde |
Nov 21 |
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Stability of minimal surfaces
Is the question: do solutions to the plateau problem in $(M,g)$ depend continuously on the metric $g$ ? If so, the answer will depend a lot on wether or not the Plateau problem has a unique solution and in which topology you measure the change in $g$ and the solution. Do you have a more precise question regarding the topologies involved ? |
Oct 21 |
answered | Calculating Exterior Distance from Measurements of Inner Geometry |
Oct 17 |
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Is there an English translation of Minding's 1839 paper?
Can you state the theorem you want more precisely ? In particular the distinction between isometric and congruent. |
Oct 8 |
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Surfaces with curvature $\leq K$ are of bounded integral curvature
Welcome to MO ! |
Sep 24 |
awarded | Necromancer |
Sep 21 |
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Did differential geometry undergo a notation change?
In the same spirit, you may have noticed that even the definition of the curvature tensor can change between modern textbooks! |
Aug 30 |
awarded | Yearling |
Jul 22 |
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Is the hypersurface satisfying $\langle x-x_0,\nu\rangle>0$ diffeomorphic to sphere?
A cylinder in $\mathbb{R}^3$ satisfies your condition (with $x_0=0$ for the cylinder $\{(x,y,z)|x^2+y^2=1\}$). Maybe you want to assume compactness of $M$ ? |