ﻻ يوجد ملخص باللغة العربية
We study singularities of Gauss maps of fronts and give characterizations of types of singularities of Gauss maps by geometric properties of fronts which are related to behavior of bounded principal curvatures. Moreover, we investigate relation between a kind of boundedness of Gaussian curvatures near cuspidal edges and types of singularities of Gauss maps of cuspidal edges. Further, we consider extended height functions on fronts with non-degenerate singular points.
In his groundbreaking work on classification of singularities with regard to right and stable equivalence of germs, Arnold has listed normal forms for all isolated hypersurface singularities over the complex numbers with either modality less than or
We prove that a class of one-dimensional maps with an arbitrary number of non-degenerate critical and singular points admits an induced Markov tower with exponential return time asymptotics. In particular the map has an absolutely continuous invarian
Let $A subset mathbb{R}^d$, $dge 2$, be a compact convex set and let $mu = varrho_0 dx$ be a probability measure on $A$ equivalent to the restriction of Lebesgue measure. Let $ u = varrho_1 dx$ be a probability measure on $B_r := {xcolon |x| le r}$ e
We give criteria for which a principal curvature becomes a bounded $C^infty$-function at non-degenerate singular points of wave fronts by using geometric invariants. As applications, we study singularities of parallel surfaces and extended distance s
We characterize plane curve germes non-degenerate in Kouchnirenkos sense in terms of characteristics and intersection multiplicities of branches.