matgaio

Rio de Janeiro, Brazil

Nov
11
comment Usefulness of Frechet versus Gateaux differentiability or something in between.
Hi! May I ask you about the explicit example on the "unfortunately" fact? Or some references? Thank you!
Aug
26
asked Geodesics of Sasaki metric
Aug
18
asked Normal fields of geodesic spheres
Aug
5
comment Normal curvature of geodesic spheres
Dear @NormalHuman, this is a nice example, thank you. I can't see if it is possible for this example to be the universal covering of a compact Riemannian manifold. If it is not, perhaps I can have some hope. I'm interested in investigate this Lipschitz constant in universal coverings of compact Riemannian manifolds without conjugate points.
Aug
4
comment Normal curvature of geodesic spheres
Hi, @AntonPetrunin, indeed. Allow me to go a little further on my question. I see that if I fix the radius $R$, the normal vector is Lipschitz as you pointed out, and it appears to me that the Lipschitz constant $L$ will depend on $R$. Letting the radius $R>1$ be arbitrary large (in the abscense of conjugate points), do you have any feeling on if it is possible to have some upper bound for the Lipschitz constants?
Aug
4
comment Normal Variation on Manifolds
Dear @AntonPetrunin, I'm interested in this sort of questions too. In particular, I've asked (math.stackexchange.com/questions/1383511/…) a related question in abscense of conjugate points. Would you mind giving me some references? Thanks a lot!
Aug
3
revised Normal curvature of geodesic spheres
edited tags
Aug
3
asked Normal curvature of geodesic spheres
Mar
22
awarded Yearling
Mar
22
awarded Yearling
Feb
24
comment a.e.-defined integrable functions on $X$.
I think the answer is the following: let us denote the domain of the function $f$ by $D(f)\subset X$. The expression "a.e.-defined integrable functions on $X$" means that $\mu\big(X-D(f)\big)=0$ and $f$ is integrable in $D(f)$
Feb
13
asked Landsberg angle
Jan
18
comment Bi-asymptotic geodesics in Visibility manifolds
Thanks again. Our conversations on the subject have opened my eyes for several points on this theory.
Jan
18
accepted Bi-asymptotic geodesics in Visibility manifolds
Jan
13
comment Bi-asymptotic geodesics in Visibility manifolds
I see. It doesn't help. I can consider just $\mathbb{H}^2\times\mathbb{R}$.
Jan
13
comment Bi-asymptotic geodesics in Visibility manifolds
I have in addition the abscense of conjugate points, if it helps...
Jan
13
revised Bi-asymptotic geodesics in Visibility manifolds
added 40 characters in body
Jan
13
comment Bi-asymptotic geodesics in Visibility manifolds
Yes, you are completely right. I have wrote (and after I deleted it) the non-compact condition, but I thought it was perhaps unnecessary to comment. I will put this there to make more sense to the question. Thanks again!
Jan
13
asked Bi-asymptotic geodesics in Visibility manifolds
Oct
29
awarded Supporter
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