A note on the backwards uniqueness of the mean curvature flow
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摘要
In this paper, we show a backwards uniqueness theorem of the mean curvature flow with bounded second fundamental forms in arbitrary codimension.
In this paper, we show a backwards uniqueness theorem of the mean curvature flow with bounded second fundamental forms in arbitrary codimension.
In this paper, we show a backwards uniqueness theorem of the mean curvature flow with bounded second fundamental forms in arbitrary codimension.
引文
1 Agmon S,Nirenberg L.Lower bounds and uniqueness theorems for solutions of differential equations in a Hilbert space.Comm Pure Appl Math,1967,20:207-229
2 Chen B L,Yin L.Uniqueness and pseudolocality theorems of the mean curvature flow.Comm Anal Geom,2007,15:435-490
3 Ecker K,Huisken G.Interior estimates for hypersurfaces moving by mean curvature.Invent Math,1991,105:547-569
4 Huang H.Backwards uniqueness of the mean curvature flow.Geom Dedicata,2019,in press
5 Huisken G.Flow by mean curvature of convex surfaces into spheres.J Differential Geom,1984,20:237-266
6 Kotschwar B.Backwards uniqueness for the Ricci flow.Int Math Res Not IMRN,2010,2010:4064-4097
7 Kotschwar B,Wang L.Rigidity of asymptotically conical shrinking gradient Ricci solitons.J Differential Geom,2015,100:55-108
8 Lee M C,Ma M.Uniqueness theorems for non-compact mean curvature flow with possibly unbounded curvatures.ArXiv:1709.00253,2017
9 Lees M,Protter M H.Unique continuation for parabolic differential equations and inequalities.Duke Math J,1961,28:369-382
10 Lin F H.A uniqueness theorem for parabolic equations.Comm Pure Appl Math,1990,43:127-136
11 Mizohata S.Unicit′e du prolongement des solutions pour quelques op′erateurs diff′erentiels paraboliques.Mem Coll Sci Univ Kyoto Ser A Math,1958,31:219-239
12 Wang L.Uniqueness of self-similar shrinkers with asymptotically conical ends.J Amer Math Soc,2014,27:613-638
13 Yamabe H.A unique continuation theorem of a diffusion equation.Ann of Math(2),1959,69:462-466
2 Chen B L,Yin L.Uniqueness and pseudolocality theorems of the mean curvature flow.Comm Anal Geom,2007,15:435-490
3 Ecker K,Huisken G.Interior estimates for hypersurfaces moving by mean curvature.Invent Math,1991,105:547-569
4 Huang H.Backwards uniqueness of the mean curvature flow.Geom Dedicata,2019,in press
5 Huisken G.Flow by mean curvature of convex surfaces into spheres.J Differential Geom,1984,20:237-266
6 Kotschwar B.Backwards uniqueness for the Ricci flow.Int Math Res Not IMRN,2010,2010:4064-4097
7 Kotschwar B,Wang L.Rigidity of asymptotically conical shrinking gradient Ricci solitons.J Differential Geom,2015,100:55-108
8 Lee M C,Ma M.Uniqueness theorems for non-compact mean curvature flow with possibly unbounded curvatures.ArXiv:1709.00253,2017
9 Lees M,Protter M H.Unique continuation for parabolic differential equations and inequalities.Duke Math J,1961,28:369-382
10 Lin F H.A uniqueness theorem for parabolic equations.Comm Pure Appl Math,1990,43:127-136
11 Mizohata S.Unicit′e du prolongement des solutions pour quelques op′erateurs diff′erentiels paraboliques.Mem Coll Sci Univ Kyoto Ser A Math,1958,31:219-239
12 Wang L.Uniqueness of self-similar shrinkers with asymptotically conical ends.J Amer Math Soc,2014,27:613-638
13 Yamabe H.A unique continuation theorem of a diffusion equation.Ann of Math(2),1959,69:462-466