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math.AP2026
Generic Mean Curvature Flow With Rough Weights
Fabius Krämer, Tim Laux, Keisuke Takasao
We prove the generic existence of mean curvature flows in spaces with rough weights. Our weak solutions are both unit-density Brakke flows and distributional solutions. Such a gene…
math.AP2026
Convergence of a vector-valued Allen-Cahn system to Brakke's multiphase mean curvature flow
Tim Laux, Keisuke Takasao
Since Ilmanen's pioneering work [J. Differential Geom. 38, 417-461, (1993)] it has been a major open problem to understand the sharp-interface limit of systems of coupled Allen-Cah…
math.AP2026
The Łojasiewicz-Simon inequality related to grain boundary motion and its applications
Masashi Mizuno, Ayumi Sakiyama, Keisuke Takasao
In this paper, we study the Łojasiewicz-Simon gradient inequality for the mathematical model of grain boundary motion. We first derive a curve shortening equation with time-depende…