Prescribing Morse scalar curvatures: Critical points at infinity

Genericity of Nondegenerate Critical Points and Morse Geodesic Functionals

We consider a family of variational problems on a Hilbert manifold parameterized by an open subset of a Banach manifold, and we discuss the genericity of the nondegeneracy condition for the critical points. Based on an idea of B. White [24], we prove an abstract genericity result that employs the infinite dimensional Sard–Smale theorem. Applications are given by proving the genericity of metric...

On Morse and other Instability Indices of Minimax Critical Points

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MATHEMA TICS: M. MORSE THE CRITICAL POINTS OF A FUNCTION OF n VARIABLES BY MARSTON MORSE

Grasp stability analysis considering the curvatures at contact points

We propose a new method for analyzing the stability of grasps. The characteristic points in this paper are to consider the curvature of both hand and object at contact points and the grasp with friction and frictionless contact. From this analysis, it is shown that the grasp using round fingers is more stable than using sharp fingers. Moreover, we establish the condition on the finger’s stiffne...

Critical Points at Infinity: a missing link in vector field topology

This paper presents an improved technique for extracting singular streamlines that extends the capabilities of vector field topology. Singular streamlines are a unique set of tangent curves that connect singular or critical points. In prior work [Ken99], we demonstrated that vector field topology (a well-known technique for extracting singular streamlines) failed to identify a class of singular...