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math.AP2018
The method of moving planes: a quantitative approach
Giulio Ciraolo, Alberto Roncoroni
We review classical results where the method of the moving planes has been used to prove symmetry properties for overdetermined PDE's boundary value problems (such as Serrin's over…
math.AP2018
Serrin's type overdetermined problems in convex cones
Giulio Ciraolo, Alberto Roncoroni
We consider overdetermined problems of Serrin's type in convex cones for (possibly) degenerate operators in the Euclidean space as well as for a suitable generalization to space fo…
math.AP2018
A remark on constant mean curvature hypersurfaces in warped product manifolds
Giulio Ciraolo, Alberto Roncoroni, Luigi Vezzoni
Alexandrov's theorem asserts that spheres are the only closed embedded constant mean curvature hypersurfaces in space forms. In this paper, we consider Alexandrov's theorem in warp…