Overdetermined problems and constant mean curvature surfaces in cones

  • Filomena Pacella

    Università di Roma La Sapienza, Italy
  • Giulio Tralli

    Università di Padova, Italy
Overdetermined problems and constant mean curvature surfaces in cones cover

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Abstract

We consider a partially overdetermined problem in a sector-like domain in a cone in , , and prove a rigidity result of Serrin type by showing that the existence of a solution implies that is a spherical sector, under a convexity assumption on the cone. We also consider the related question of characterizing constant mean curvature compact surfaces with boundary which satisfy a 'gluing' condition with respect to the cone . We prove that if either the cone is convex or the surface is a radial graph then must be a spherical cap. Finally we show that, under the condition that the relative boundary of the domain or the surface intersects orthogonally the cone, no other assumptions are needed.

Cite this article

Filomena Pacella, Giulio Tralli, Overdetermined problems and constant mean curvature surfaces in cones. Rev. Mat. Iberoam. 36 (2020), no. 3, pp. 841–867

DOI 10.4171/RMI/1151