Pairs of Embedded Spheres with Pinched Prescribed Mean Curvature
Abstract
Assume h is a positive function on the unit three-sphere which satisfies the pinching condition h < h0 ≈ 0.547. We prove the existence of at least two embedded two-spheres with prescribed mean curvature h. The same result holds for sign-changing functions h satisfying h < h0 under a mild assumption on the zero set.
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