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arXiv · 1709.08495

Embedded tori with prescribed mean curvature

Paolo Caldiroli·Monica Musso
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Abstract

We construct a sequence of compact, oriented, embedded, two-dimensional surfaces of genus one into Euclidean 3-space with prescribed, almost constant, mean curvature of the form $H(X)=1+{A}{|X|^{-\gamma}}$ for $|X|$ large, when $A<0$ and $\gamma\in(0,2)$. Such surfaces are close to sections of unduloids with small necksize, folded along circumferences centered at the origin and with larger and larger radii. The construction involves a deep study of the corresponding Jacobi operators, an application of the Lyapunov-Schmidt reduction method and some variational argument.

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Paolo Caldiroli, Monica Musso. 2017-09-25. Embedded tori with prescribed mean curvature. https://arxiv.org/abs/1709.08495

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