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arXiv · 2312.12375

Perturbed cone theorems for proper harmonic maps

Renan Assimos·Balázs Márk Békési·Giuseppe Gentile
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Abstract

Inspired by the halfspace theorem for minimal surfaces in $\mathbb{R}^3$ of Hoffman-Meeks, the halfspace theorem of Rodriguez-Rosenberg, and the cone theorem of Omori, we derive new non-existence results for proper harmonic maps into perturbed cones in $\mathbb{R}^n$, horospheres in $\mathbb{H}^n$ and also into perturbed Riemannian cones. The technical tool in use is an extension of the foliated maximum principle appearing in Assimos-Jost to the non-compact setting.

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Renan Assimos, Balázs Márk Békési, Giuseppe Gentile. 2023-12-19. Perturbed cone theorems for proper harmonic maps. https://doi.org/10.4153/s0008439525101367

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