NDLI: Curvature and distance function from a manifold

Content Provider	Springer Nature Link
Author	Ambrosio, Luigi Mantegazza, Carlo
Copyright Year	1998
Abstract	This paper is concerned with the relations between the differential invariants of a smooth manifold embedded in the Euclidean space and the square of the distance function from the manifold. In particular, we are interested in curvature invariants like the mean curvature vector and the second fundamental form. We find that these invariants can be computed in a very simple way using the third order derivatives of the squared distance function. Moreover, we study a general class of functionals depending on the derivatives up to a given order γ of the squared distance function and we find an algorithm for the computation of the Euler equation. Our class of functionals includes as particular cases the well-known area functional (γ = 2), the integral of the square of the quadratic norm of the second fundamental form (γ = 3), and the Willmore functional.
Starting Page	723
Ending Page	748
Page Count	26
File Format	PDF
ISSN	10506926
Journal	Journal of Geometric Analysis
Volume Number	8
Issue Number	5
e-ISSN	1559002X
Language	English
Publisher	Springer-Verlag
Publisher Date	1998-01-01
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	distance function second fundamental form Willmore functional Differential Geometry Convex and Discrete Geometry Fourier Analysis Abstract Harmonic Analysis Dynamical Systems and Ergodic Theory Global Analysis and Analysis on Manifolds
Content Type	Text
Resource Type	Article
Subject	Geometry and Topology

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