Gauss Rigidity and Volume Preservation Under Preserving Curvature Deformations for Hedgehogs

Autor:	Yves Martinez-Maure
Rok vydání:	2012
Předmět:	Applied Mathematics Gauss Mathematical analysis Regular polygon Rigidity (psychology) Curvature symbols.namesake Mathematics (miscellaneous) Minkowski space Gaussian curvature symbols Differentiable function Constant (mathematics) Mathematical physics Mathematics
Zdroj:	Results in Mathematics. 63:973-983
ISSN:	1420-9012 1422-6383
DOI:	10.1007/s00025-012-0248-8
Popis:	We consider Gauss rigidity and Gauss infinitesimal rigidity for hedgehogs of \({\mathbb{R}^{3}}\) (regarded as Minkowski differences of closed convex surfaces of \({\mathbb{R}^{3}}\) with positive Gaussian curvature). Besides, we prove under an appropriate differentiability condition that whenever we perform a deformation of a hedgehog so that its curvature function remains constant, its algebraic volume also remains constant.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::2adf82b7ee6b880c8c6f746316dda7ef https://doi.org/10.1007/s00025-012-0248-8 Zobrazit plný text záznamu Full text from SpringerLink