Mean curvature, threshold dynamics, and phase field theory on finite graphsTools van Gennip, Yves and Guillen, Nestor and Osting, Braxton and Bertozzi, Andrea L. (2014) Mean curvature, threshold dynamics, and phase field theory on finite graphs. Milan Journal of Mathematics, 82 (1). pp. 365. ISSN 14249286
Official URL: http://dx.doi.org/10.1007/s0003201402168
AbstractIn the continuum, close connections exist between mean curvature flow, the AllenCahn (AC) partial differential equation, and the MerrimanBenceOsher (MBO) threshold dynamics scheme. Graph analogues of these processes have recently seen a rise in popularity as relaxations of NPcomplete combinatorial problems, which demands deeper theoretical underpinnings of the graph processes. The aim of this paper is to introduce these graph processes in the light of their continuum counterparts, provide some background, prove the first results connecting them, illustrate these processes with examples and identify open questions for future study.
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