Homotopic distance between maps

On Homotopic Harmonic Maps

(1.1) M' is complete and its sectional curvatures are non-positive. In terms of local coordinates x = (x, . . . , x) on M and y = (y, . . . , y) on M', let the respective Riemann elements of arc-length be ds = gij dx dx\ ds' = g'a$ dy a dy& and r^-fc, T'Vy be the corresponding Christoffel symbols. When there is no danger of confusion, x (or y) will represent a point of M (or M') or its coordina...

Minimizing energy among homotopic maps

Homotopic Transformations of Combinatorial Maps

In this contribution, we propose the notion of homotopy for both combinatorial maps and weighted combinatorial maps. We also describe transformations that are homotopic in the defined sense. The usefulness of the concept introduced is illustrated using two applications. The first one consists in calculating a skeleton using homotopic transformations of weighted combinatorial maps. The result is...

A distance measure between labeled combinatorial maps

Combinatorial maps are widely used in image representation and processing, however map matching problems have not been extensively researched. This paper addresses the problem of inexact matching between labeled combinatorial maps. First, the concept of edit distance is extended to combinatorial maps, and then used to define mapping between combinatorial maps as a sequence of edit operations th...

Criteria for Homotopic Maps to be So Along Monotone Homotopies

The state spaces of machines admit the structure of time. A homotopy theory respecting this additional structure can detect machine behavior unseen by classical homotopy theory. In an attempt to bootstrap classical tools into the world of abstract spacetime, we identify criteria for classically homotopic, monotone maps of pospaces to future homotope, or homotope along homotopies monotone in bot...