Journal of Convex Analysis 29 (2022), No. 2, 391--410
Copyright Heldermann Verlag 2022
On the Square Distance Function from a Manifold with Boundary
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
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.
Keywords: Square distance function, smooth manifolds with boundary, signed distance function.
MSC: 53A07; 51K05.
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