A notion of robustness and stability of manifolds
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Dosyalar
Tarih
2008-06-01
Yazarlar
Dergi Başlığı
Dergi ISSN
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Yayıncı
Academic Press Inc Elsevier Science
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
Starting from the notion of thickness of Parks we define a notion of robustness for arbitrary subsets of R-k and we investigate its relationship with the notion of positive reach of Federer. We prove that if a set M is robust, then its boundary a M is of positive reach and conversely (under very mild restrictions) if partial derivative M is of positive reach, then M is robust. We then prove that a closed non-empty robust set in R-k (different from R-k) is a codimension zero submanifold of class C-1 with boundary. As a partial converse we show that any compact codimension zero submanifold with boundary of class C-2 is robust. Using the notion of robustness we prove a kind of stability theorem for codimension zero compact submanifolds with boundary: two such submanifolds, whose boundaries are close enough (in the sense of Hausdorff distance), are diffeomorphic. (C) 2007 Elsevier Inc. All rights reserved.
Açıklama
Anahtar Kelimeler
thickness, positive reach, stability of manifolds, Hausdortf distance
Kaynak
Journal Of Mathematical Analysis And Applications
WoS Q Değeri
Q1
