Tagged Questions
1
vote
0answers
30 views
Minimum is attained in a subset of a Sobolev space
Let $\Omega \subset \mathbb R^n$. I have a functional of the form,
$$\int_{\Omega}f(x,u,\nabla u)dx$$
where $u \in W^{1,p}(\Omega, M)$, $M \subset \mathbb R^d$ is a compact, smooth Riemannian ...
0
votes
0answers
39 views
A problem about geodesics in a manifold $M$ diffeomorphic to $\mathbb S^2$
I am now reading the book Calculus of Variations written by Jost and I encountered the following problem (in Theorem 2.3.3.):
Let $M$ be a differentiable submanifold of $\mathbb R^d$ diffeomorphic to ...
3
votes
1answer
73 views
Geodesics in a manifold M diffeomorphic to $\mathbb S^2$
I am now reading the book Calculus of Variations written by Jost and I encountered the following problem (in Theorem 2.3.3.):
Let $M$ be a differentiable submanifold of $\mathbb R^d$ diffeomorphic to ...
0
votes
1answer
70 views
Simplifying the search for a geodesic
How can calculations for the geodesics on the surface $U=\{(x,y,z): c(x^2+y^2)-z^2=0, z>0\}$ be simplified by noting that is locally Euclidean? I can see that the property means that when we open ...
