All Questions
7 questions
1
vote
0
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114
views
Has this logarithmic volume functional been studied?
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\newcommand{\VolN}{\text{Vol}_{\N}}$
This question is mainly a reference request. (It is a cross-post ...
- 6,741
4
votes
0
answers
244
views
A simple proof that all the symmetries of the Dirichlet energy are conformal
This is a cross-post.
It seems to be folklore knowledge that all the (source) symmetries of the $d$-Dirichlet energy are conformal maps.
Specifically, I have found this nice proof for the following ...
- 6,741
4
votes
0
answers
140
views
Has this functional been studied?
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This is a cross-post from MSE.
Let $\M,\N$ be Riemannian ...
- 6,741
6
votes
2
answers
207
views
Are all symmetries of the Dirichlet functional isometries?
This is a cross-post from MSE (no answer there).
Let $M,N$ be oriented $d$-dimensional Riemannian manifolds, $M$ compact*, and let $f:M \to N$ be smooth.
Consider the Dirichlet energy functional: $...
- 6,741
13
votes
1
answer
739
views
Is this expression for the Laplacian of conformal maps between Riemannian manifolds known?
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- 6,741
5
votes
2
answers
730
views
Good references on the theory of harmonic mappings between Riemannian manifolds
I am currently reading the book by Professor Jost, "Riemannian geometry and geometric analysis", the last chapter on harmonic maps. It talks mainly about existence and regularity of the theory of ...
- 1,881
3
votes
0
answers
96
views
Invariant Lagrangians of a connection and its derivatives: how do they look like?
Let
$$
L=L(\Gamma,\partial\Gamma,\ldots,\partial^n\Gamma)
$$
be a Lagrangian depending on a linear symmetric connection $\Gamma$ on the tangent space of a manifold $M$ together with its derivatives up ...
- 2,527