6533b861fe1ef96bd12c4608

RESEARCH PRODUCT

The method of moving planes: a quantitative approach

Giulio CiraoloAlberto Roncoroni

subject

Mathematics - Differential Geometryoverdetermined problem010102 general mathematicsmean curvaturelcsh:QA299.6-43335N25; 35B35; 53A10; 53C24; 35B50; 35B51; 35J70alexandrov soap bubble theoremlcsh:Analysisstability01 natural sciencesAlexandrov Soap Bubble Theorem; overdetermined problems; rigidity; stability; mean curvature; moving planesMathematics - Analysis of PDEsrigidityDifferential Geometry (math.DG)Settore MAT/05 - Analisi Matematicaoverdetermined problemsFOS: Mathematics0101 mathematicsmoving planesAnalysis of PDEs (math.AP)

description

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 overdetermined problem) and for rigidity problems in geometric analysis (like Alexandrov soap bubble Theorem), and we give an overview of some recent results related to quantitative studies of the method of moving planes, where quantitative approximate symmetry results are obtained.

yearjournalcountryeditionlanguage
2018-01-01
http://arxiv.org/abs/1811.05202