Premium
Some Consequences of the Nature of the Distance Function on the Cut Locus in a Riemannian Manifold
Author(s) -
Barden Dennis,
Le Huiling
Publication year - 1997
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s002461079700553x
Subject(s) - locus (genetics) , mathematics , differentiable function , neighbourhood (mathematics) , riemannian manifold , pure mathematics , manifold (fluid mechanics) , conjugate points , function (biology) , mathematical analysis , combinatorics , evolutionary biology , biology , gene , mechanical engineering , biochemistry , chemistry , engineering
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.