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Results tagged with curvature
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user 13093
Gaussian curvature, mean curvature, sectional curvature, scalar curvature, curvature tensors (Riemann, Ricci, Weyl)
1
vote
1
answer
47
views
Approximation with a more regular function and an inequality constraint
The motivation of the question comes from a geometric problem: can we approximate a $C^{1,\alpha}$ set $\Omega$ with positive curvature (in distributional sense) from inside with $C^2$ sets with positive … curvature? …
- 2,222
0
votes
Accepted
Approximation with a more regular function and an inequality constraint
In fact the question is equivalent to the following one: Regularization by mean curvature flow
Take a look at the article in the given answer to see the proof. …
- 2,222
6
votes
1
answer
311
views
Regularization by mean curvature flow
The fact that the initial condition has non-negative mean curvature should be preserved under the flow, so $\phi_t$ will have non-negative mean curvature. … On the other hand the bound on the curvature of the initial condition should give a finite upper bound for the curvature of $\phi_t$ (for small $t$). …
- 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