The subject of motion by crystalline curvature is of interest for three quite distinct reasons. One is that some physical surface energies and physical models of crystal growth simply do give rise to such motion. Another is its use as a way to approximate motion of curves by curvature, both for computation and possibly for proving theorems. The third is that this motion simply is interesting and beautiful in its own right, having results that sometimes parallel those for ordinary curvature and sometimes are strikingly different.

What It Means

This is a placeholder explanation generated by the low-overhead model. It interprets "The subject of motion by crystalline curvature is of interest for three quite distinct reasons. One is that some physical surface energies and physical models of crystal growth simply do give rise to such motion. Another is its use as a way to approximate motion of curves by curvature, both for computation and possibly for proving theorems. The third is that this motion simply is interesting and beautiful in its own right, having results that sometimes parallel those for ordinary curvature and sometimes are strikingly different." in the context of "(1993), Differential Geometry: Partial Differential Equations on Manifolds chapter: Motion of curves by crystalline curvature, including triple junctions and boundary points by Jean E. Taylor, pages: 417–438, publisher: American Mathematical Soc., ISBN: 978-0-8218-1494-9, series: Proc. Symp. Pure Math, vol. 54, Part 1 (quote from p. 417)" to mean that wisdom is timeless.