Geodesic
Stabilization technique applied to curve shortening flow in the plane
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 45, Tome 444 (2016), pp. 89-97 
H. Mikayelyan. Stabilization technique applied to curve shortening flow in the plane. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 45, Tome 444 (2016), pp. 89-97. http://geodesic.mathdoc.fr/item/ZNSL_2016_444_a3/
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

The method proposed by T. I. Zelenjak is applied to the mean curvature flow in the plane. A new type of monotonicity formula for star-shaped curves is obtained.

[1] M. Gage, R. Hamilton, “The heat equation shrinking convex plane curves”, J. Differential Geom., 23:1 (1986), 69–96 | MR | Zbl

[2] M. Grayson, “The heat equation shrinks embedded plane curves to round points”, J. Differential Geom., 26:2 (1987), 285–314 | MR | Zbl

[3] G. Huisken, “Flow by mean curvature of convex surfaces into spheres”, J. Differential Geom., 20:1 (1984), 237–266 | MR | Zbl

[4] G. Huisken, “Asymptotic behavior for singularities of the mean curvature flow”, J. Differential Geom., 31:2 (1991), 285–299 | MR

[5] T. I. Zelenjak, “Stabilization of solutions of boundary value problems for a second-order parabolic equation with one space variable”, Differencialnye Uravnenija, 4 (1968), 34–45 | MR

[6] Xi-Ping Zhu, Lectures on mean curvature flows, AMS/IP Studies in Advanced Mathematics, 32, American Mathematical Society, Providence, RI, 2002, x+150 pp. | MR | Zbl