Alexandrov's soap bubble theorem

Alexandrov's soap bubble theorem is a mathematical theorem from geometric analysis that characterizes a sphere through the mean curvature. The theorem was proven in 1958 by Alexander Danilovich Alexandrov.[1][2] In his proof he introduced the method of moving planes, which was used after by many mathematicians successfully in geometric analysis.

Soap bubble theorem

Let be a bounded connected domain with a boundary that is of class with a constant mean curvature, then is a sphere.[3][4]

Literature
  • Ciraolo, Giulio; Roncoroni, Alberto (2018). "The method of moving planes: a quantitative approach". p. 1. arXiv:1811.05202.
  • Smirnov, Yurii Mikhailovich; Aleksandrov, Alexander Danilovich (1962). "Nine Papers on Topology, Lie Groups, and Differential Equations". American Mathematical Society Translations. 2. Vol. 21. American Mathematical Soc. ISBN 0821817213.

References
  1. Alexandrov, Alexander Danilovich (1962). "Uniqueness theorem for surfaces in the large". American Mathematical Society Translations. 2. Vol. 21. American Mathematical Soc. pp. 412–416.
  2. Alexandrov, Alexander Danilovich (1962). "A characteristic property of spheres". Annali di Matematica. 58: 303–315. doi:10.1007/BF02413056.
  3. Magnanini, Rolando; Poggesi, Giorgio (2017). "Serrin's problem and Alexandrov's Soap Bubble Theorem: enhanced stability via integral identities". Indiana University Mathematics Journal. 69. arXiv:1708.07392. doi:10.1512/iumj.2020.69.7925.
  4. Ciraolo, Giulio; Roncoroni, Alberto (2018). "The method of moving planes: a quantitative approach". p. 1. arXiv:1811.05202.
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