In this paper,the curve shortening flow in a general Riemannian manifold is studied,Altschuler’s results about the flow for space curves are generalized.For any n-dimensional(n ≥ 2)Riemannian manifold(M,g) with some...In this paper,the curve shortening flow in a general Riemannian manifold is studied,Altschuler’s results about the flow for space curves are generalized.For any n-dimensional(n ≥ 2)Riemannian manifold(M,g) with some natural assumptions,we prove the planar phenomenon when the curve shortening flow blows up.展开更多
基金Supported by NSFC (Grant No. 11721101)National Key Research and Development Project SQ2020YFA070080。
文摘In this paper,the curve shortening flow in a general Riemannian manifold is studied,Altschuler’s results about the flow for space curves are generalized.For any n-dimensional(n ≥ 2)Riemannian manifold(M,g) with some natural assumptions,we prove the planar phenomenon when the curve shortening flow blows up.
