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Results tagged with dg.differential-geometry
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user 13093
Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis.
15
votes
1
answer
2k
views
Car movement - differential geometry interpretation.
I've posted this on Math Stack Exchange and I didn't get any answer in a couple of days, so I'll try and post it here too.
The problem presented below is from my differential geometry course. The ini …
- 2,222
5
votes
2
answers
293
views
Simplification of integral on the sphere
In the article: https://arxiv.org/abs/0906.3217 the authors prove in Lemma 1 a formula which helps compute more easily the integral of the Hessian of a function defined on $\Bbb{S}^2$. More precisely, …
- 2,222
1
vote
Regularity - mean curvature equation
This question is solved in the PhD thesis of Nicolas Landais: Problèmes de régularité en optimisation de forme. You can read the thesis here. The result is presented in Chapter 6. The conclusion is th …
- 2,222
1
vote
1
answer
341
views
Singular conformally-Euclidean metrics
Suppose $W : \Bbb{R}^n \to \Bbb{R}_+$ is a continuous, positive function, with exactly $n$ zeros $\alpha_1,...,\alpha_n$. Define the following 'distance':
$$ d(\alpha_i,\alpha_j)=\inf\{\int_0^1 \sqrt …
- 2,222
1
vote
Multiplicity of Laplace eigenvalues and symmetry
When minimizing numerically the eigenvalues of the Laplacian under area constraint in 2D it is observed that optimal shapes tend to have multiple eigenvalues. Take for example the simulations shown he …
- 2,222