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SOME CONSEQUENCES OF THE NATURE OF THE DISTANCE FUNCTION ON THE CUT LOCUS IN A RIEMANNIAN MANIFOLD

Published online by Cambridge University Press:  01 October 1997

DENNIS BARDEN  and
HUILING LE
DENNIS BARDEN
Affiliation:
Girton College, Cambridge CB3 0JG
HUILING LE
Affiliation:
Department of Mathematics, University of Nottingham, University Park, Nottingham NG7 2RD
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Abstract

We render the cut locus more accessible to analysis by showing that each non-conjugate cut point has a neighbourhood on which the distance function is the minimum of finitely many smooth ‘radial functions’. This enables us to generalise to an arbitrary complete manifold a number of recent results, mainly from stochastic analysis, which were either limited or not valid on the cut locus because of the lack of differentiability there of the distance function.

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 56 , Issue 2 , October 1997 , pp. 369 - 383
Copyright
The London Mathematical Society 1997

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