# Existence of constant mean curvature 2-spheres in Riemannian 3-spheres

@inproceedings{Cheng2020ExistenceOC, title={Existence of constant mean curvature 2-spheres in Riemannian 3-spheres}, author={Da Rong Cheng and Xin Zhou}, year={2020} }

We prove the existence of branched immersed constant mean curvature 2spheres in an arbitrary Riemannian 3-sphere for almost every prescribed mean curvature, and moreover for all prescribed mean curvatures when the 3-sphere is positively curved. To achieve this, we develop a min-max scheme for a weighted Dirichlet energy functional. There are three main ingredients in our approach: a bi-harmonic approximation procedure to obtain compactness of the new functional, a derivative estimate of the min…

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