Conformal embeddings of $S^2\to\mathbb{R}^3$ with prescribed mean curvature: A variational approach

Tian Xu

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arXiv · 1810.03874

Conformal embeddings of $S^2\to\mathbb{R}^3$ with prescribed mean curvature: A variational approach

Tian Xu

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Abstract

Motivated by recent progress on a spinorial analogue of the Yamabe problem in the geometric literature, we study a conformally invariant spinor field equation on the $m$-sphere, $m\geq2$. Via variational methods and the spinorial Weierstraß representation, we study the problem of prescribing mean curvature for the immersion $S^2\to\mathbb{R}^3$.

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Tian Xu. 2022-02-11. Conformal embeddings of $S^2\to\mathbb{R}^3$ with prescribed mean curvature: A variational approach. https://arxiv.org/abs/1810.03874

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