On the Square Distance Function from a Manifold with Boundary

Giovanni Bellettini; Alaa Elshorbagy

Abstract

We characterize arbitrary codimensional smooth manifolds M with boundary embedded in Rn using the square distance function from M and from its boundary. The results are localized in an open set.

Author information

Contact details are reproduced from the original publication and may be historical.

Giovanni Bellettini

Dip. di Ingegneria dell'Informazione e Scienze Matematiche, Università di Siena, Italy
and: International Centre for Theoretical Physics, Mathematics Section, Trieste, Italy

bellettini@diism.unisi.it

Alaa Elshorbagy

Area of Mathematical Analysis, Modelling and Applications, SISSA, Trieste, Italy
and: International Centre for Theoretical Physics, Mathematics Section, Trieste, Italy

alaa.elshorbagy@sissa.it

Keywords

Square distance function
smooth manifolds with boundary
signed distance function

Mathematics Subject Classification

53A07; 51K05

Suggested citation

G. Bellettini, A. Elshorbagy. “On the Square Distance Function from a Manifold with Boundary.” Journal of Convex Analysis 29 (2022), No. 2, 391–410.