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Manifolds with Boundary and of Bounded Geometry
Author(s) -
Schick Thomas
Publication year - 2001
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/1522-2616(200103)223:1<103::aid-mana103>3.0.co;2-s
Subject(s) - mathematics , bounded function , geodesic , geometry , boundary (topology) , atlas (anatomy) , partition (number theory) , curvature , riemannian geometry , riemann curvature tensor , mathematical analysis , combinatorics , paleontology , biology
For non–compact manifolds with boundary we prove that bounded geometry defined by coordinate–free curvature bounds is equivalent to bounded geometry defined using bounds on the metric tensor in geodesic coordinates. We produce a nice atlas with subordinate partition of unity on manifolds with boundary of bounded geometry and we study the change of geodesic coordinate maps.