Differentiability conditions and bounds on singular points

Generalized Helices and Singular Points

In this paper, we define X-slant helix in Euclidean 3-space and we obtain helix, slant helix, clad and g-clad helix as special case of the X-slant helix. Then we study Darboux, tangential darboux developable surfaces and their singular points. Especially we show that the striction lines of these surfaces are singular locus of the surfaces.

On the differentiability conditions at spacelike infinity

We consider space-times which are asymptotically flat at spacelike infinity, i. It is well known that, in general, one cannot have a smooth differentiable structure at i, but have to use direction dependent structures. Instead of the oftenly used C-differentiabel structure, we suggest a weaker differential structure, a C + structure. The reason for this is that we have not seen any completions ...

Differentiability of themetric projection onto a convex set with singular boundary points

The differentiability of the metric projection P onto a closed convex set K in Rn is examined. The boundary ãK can have singular points of orders k ̈ −1Ù 0Ù 1ÜÙ n − 1. Here k ̈ −1 corresponds to the interior points of K , k ̈ 0 to regular points of the boundary (i.e., faces), k ̈ 1ÙÜ Ù n − 2 to edges and k ̈ n − 1 to vertices. It is assumed that for every k the set of all singular points forms ...

Non-differentiability points of Cantor functions

Critical Points of Functions on Singular Spaces

We compare and contrast various notions of the “critical locus” of a complex analytic function on a singular space. After choosing a topological variant as our primary notion of the critical locus, we justify our choice by generalizing Lê and Saito’s result that constant Milnor number implies that Thom’s af condition is satisfied.