1,712 reputation
1818
bio website perso-math.univ-mlv.fr/users/…
location Créteil
age 30
visits member for 4 years, 7 months
seen 2 hours ago

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
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.
Nov
28
answered Frobenius Condition for a specific first order pde
Nov
21
comment 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
comment 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
comment Surfaces with curvature $\leq K$ are of bounded integral curvature
Welcome to MO !
Sep
24
awarded  Necromancer
Sep
21
comment 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
comment 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 $M$ ?