一个拟共形的Hopf肥皂泡定理
A quasiconformal Hopf soap bubble theorem
摘要：
本文证明了欧氏空间中亏格为零的紧致曲面满足其主曲率之间的拟共形不等式时是圆球。这解决了H.霍普夫，并给出了一个球形版本的西蒙的拟共形伯恩斯坦定理。该结果推广了常中曲率球面的Hopf定理，将圆球分类为亏格为零的唯一紧致椭圆Weingarten曲面，以及Han，Nadirashvili和Yuan的卵形唯一性定理.证明依赖于具有间断系数的线性椭圆型方程解的Bers-Nirenberg表示。
英文摘要：
We show that any compact surface of genus zero in Euclidean 3-space that satisfies a quasiconformal inequality between its principal curvatures is a round sphere. This solves an old open problem by H. Hopf, and gives a spherical version of Simon's quasiconformal Bernstein theorem. The result generalizes, among others, Hopf's theorem for constant mean curvature spheres, the classification of round spheres as the only compact elliptic Weingarten surfaces of genus zero, and the uniqueness theorem for ovaloids by Han, Nadirashvili and Yuan. The proof relies on the Bers-Nirenberg representation of solutions to linear elliptic equations with discontinuous coefficients.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
