1,782 reputation
1820
bio website perso-math.univ-mlv.fr/users/…
location Créteil
age 30
visits member for 4 years, 10 months
seen 1 min ago

Now at "Université Paris Est Créteil". I work in Riemannian geometry, and more specifically on Ricci flow.


Jun
11
answered Gauss-Bonnet formula for 2-dimensional Alexandrov spaces
Jun
11
comment Gauss-Bonnet formula for 2-dimensional Alexandrov spaces
Existence is known, I'm currently writing an answer about it.
Jun
11
comment Gauss-Bonnet formula for 2-dimensional Alexandrov spaces
Actually in this context, just requiring that the curvature measure is not zero and nonnegative should be enough (which is weaker than what you require, there could be dirac masses in the curvature, think about the surface of a cube for instance).
Jun
11
comment Gauss-Bonnet formula for 2-dimensional Alexandrov spaces
For question 2, you need to require that the curvature is not everywhere 0 to exclude the torus.
May
1
awarded  Nice Answer
Apr
30
awarded  Popular Question
Apr
1
comment Shortest paths in Alexandrov spaces
@valeri why don't you make this an answer ?
Apr
1
comment Thales Style Level Sets
I can write down an explicit formula in finite time for plane polygons, but it will be ugly...
Mar
31
comment Thales Style Level Sets
Except the original motivation, is it that important to restrict the question to plane 2-dimensional figures ? (Actually the only sets for which I can answer the question are balls !)
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
comment 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.