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Some results on minimal barriers in the sense of De Giorgi applied to driven motion by mean curvature. (English) Zbl 0944.53039
Authors’ abstract: “We prove some properties of the minimal barriers in the sense of De Giorgi for the driven mean curvature flow in codimension one. We compare the resulting evolution with an abstract evolution, and in particular with the evolution defined with the methods of L. C. Evans and J. Spruck [J. Differ. Geom. 33, 635-681 (1971; Zbl 0726.53029), Trans. Am. Math. Soc. 330, 321-332 (1992; Zbl 0776.53005) and J. Geom. Anal. 2, 121-150 (1992; Zbl 0768.53003)], Y.-G. Chen, Y. Giga and S. Goto [J. Differ. Geom. 33, 749-786 (1991; Zbl 0696.35087)], and Y. Giga, S. Goto, H. Ishii and M.-H. Sato [Indiana Univ. Math. J. 40, 443-470 (1991; Zbl 0836.35009)]”.

53C44 Geometric evolution equations (mean curvature flow, Ricci flow, etc.) (MSC2010)