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

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, $m\ge 2$. Via variational methods and the spinorial Weierstraß representation, we study the problem of prescribing mean curvature for the immersion $S^2\to {\mathbb{R}}^3$.