Special solutions to a geometric curvature flow of evaporation–condensation
Year: 2025
Type: article
Abstract: In this paper we study the evolution of special hypersurfaces in Euclidean space evolving according to a geometric curvature flow which is motivated from the phenomenon of evaporation-condensation and which was introduced in Mullins (1957). The first example is a closed, embedded and convex curve which does not converge to a point under the (smooth) flow. This shows that the flow behaves differently from curve shortening flow. Further we show existence of two examples of hypersurfaces which translate under this evolution. Their shape is motivated from translators as they appear in the theory of mean curvature flow: A complete, unbounded graph over a finite time interval and in the higher dimensional case a rotationally symmetric entire graph over R n .
Source: Physica D Nonlinear Phenomena
Authors: Axel Kröner, Heiko Kröner
Institution: Martin Luther University Halle-Wittenberg
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,640
OpenAlex ID: W4416548898