Contents 11 4. Equivalence of the two constraints 14 5. Convergence of the non-contact set 15 6. Semiconcavity 16 7. Convergence of the gradients 21 7.1. Lower semicontinuity 21 7.2. Proof of Theorem 1.3 (T6) 22 Appendix A. Appendix about semiconcavity 22 Appendix B. A counter-example to the equivalence of (1.3) and (1.14) for small m 23 References 25
We propose a new method for the numerical computation of the cut locus of a compact submanifold of R3
without boundary. This method is based on a convex variational problem with conic constraints, with proven convergence. We illustrate the versatility of our approach by the approximation of Voronoi cells on embedded surfaces of R3.
We consider the volume-constrained minimization of the sum of the perimeter and the Riesz potential. We add an external potential of the form |x| β that provides the existence of a minimizer for any volume constraint, and we study the geometry of large volume minimizers. Then we provide a numerical method to address this variational problem. arXiv:1707.06028v2 [math.OC]
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