Continuous Functions Induced by Shape Morphisms

Filtrations induced by continuous functions

In Persistent Homology and Topology, filtrations are usually given by introducing an ordered collection of sets or a continuous function from a topological space to R. A natural question arises, whether these approaches are equivalent or not. In this paper we study this problem and prove that, while the answer to the previous question is negative in the general case, the approach by continuous ...

Harmonic morphisms and subharmonic functions

Let M be a complete Riemannian manifold and N a complete noncompact Riemannian manifold. Let φ : M → N be a surjective harmonic morphism. We prove that if N admits a subharmonic function with finite Dirichlet integral which is not harmonic, and φ has finite energy, then φ is a constant map. Similarly, if f is a subharmonic function on N which is not harmonic and such that |df | is bounded, and ...

Contra $beta^{*}$-continuous and almost contra $beta^{*}$-continuous functions

The notion of contra continuous functions was introduced and investigated by Dontchev. In this paper, we apply the notion of $beta^{*}$-closed sets in topological space to present and study a new class of functions called contra $beta^{*}$-continuous and almost contra $beta^{*}$-continuous functions as a new generalization of contra continuity.

Morphisms of Mislin Genera Induced by Finite Normal Subgroups

Continuous Deformations by Isometry Preserving Shape Integration

We introduce a novel continuous surface deformation method which relies on a time-dependent vector field over a triangular mesh. For every time step the piecewise linear vector field is obtained by leastsquares minimization of the metric distortion induced by integration subject to boundary conditions. As an integral part of the approach, we introduce a new measure to describe local metric dist...