Critical points of simple functions

Critical points of simple functions

On the Critical Points of Harmonic 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.

A NOTE ON SIMPLE a-POINTS OF L-FUNCTIONS

We prove, subject to certain hypotheses, that a positive proportion of the a-points of the Riemann zeta-function and Dirichlet L-functions with primitive characters are simple and discuss corresponding results for other functions in the Selberg class. We also prove an unconditional result of this type for the a-points in fixed strips to the right of the line s = 1/2.

On Improving the Search for Critical Points of Implicit Functions

Recently, there is a trend to develop efficient polygonization techniques for implicit surfaces, aiming at interactive modeling and animation. One of the most challenging issues for such techniques is to ensure the matching between the topology of the surface and the topology of its polygonal approximation. Therefore, it is important to accurately extract the topological information from a give...