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pro vyhledávání: '"Sarnataro, Lorenzo"'
We prove upper bounds for the Morse index and number of intersections of min-max geodesics achieving the $p$-widths of a closed surface. A key tool in our analysis is a proof that for a generic set of metrics, the tangent cone at any vertex of any fi
Externí odkaz:
http://arxiv.org/abs/2410.02580
We study the boundary behavior of any limit-interface arising from a sequence of general critical points of the Allen-Cahn energy functionals on a smooth bounded domain. Given any such sequence with uniform energy bounds, we prove that the limit-inte
Externí odkaz:
http://arxiv.org/abs/2312.07210
Autor:
Sarnataro, Lorenzo, Stryker, Douglas
We find conditions under which Almgren-Pitts min-max for the prescribed geodesic curvature functional in a closed oriented Riemannian surface produces a closed embedded curve of constant curvature. In particular, we find a closed embedded curve of an
Externí odkaz:
http://arxiv.org/abs/2306.04840
Autor:
Sarnataro, Lorenzo, Stryker, Douglas
We prove the optimal $C^{1,1}$ regularity for minimizers of the prescribed mean curvature functional over isotopy classes. As an application, we find an embedded sphere of prescribed mean curvature in the round 3-sphere for an open dense set of presc
Externí odkaz:
http://arxiv.org/abs/2304.02722
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