Local Techniques for Mean Curvature Flow
نویسنده
چکیده
of ann-dimensional manifold without boundary into Euclidean space. We say Af = x(Mn) moves by mean curvature if there exists a one-parameter family Xt = x( ·, t) of immersions with corresponding images J..!I1 = x 1(lvfn) satisfying d dtx(p,t) = -H(p,t)v(p,t) (1) x(p,O) = xo(P) for some initial data xo. Here H(p,t) and v(p,t) denote mean curvature and outer unit normal of the hypersurface M 1 at x(p, t). Using the well-known formula .0-x = -Hv for hypersurfaces Af in R n+I we obtain the parabolic system of differential equations
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