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학술연구/단체지원/교육 등 연구자 활동을 지속하도록 DBpia가 지원하고 있어요.
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연구자들이 자신의 연구와 전문성을 널리 알리고, 새로운 협력의 기회를 만들 수 있는 네트워킹 공간이에요.
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In this paper we consider the evolution of the rolling stone with a rotationally symmetric nonconvex compact initial surface 0 under the Gauss curvature ow. Let X : Sn [0,1) ! Rn+1 be the embeddings of the sphere in Rn+1 such that (t) = X(Sn, t) is the surface at time t and (0) = 0. As a consequence the parabolic equation describing the motion of the hypersurface becomes degenerate on the interface sep-arating the nonconvex part from the strictly convex side, since one of the curvature will be zero on the interface. By expressing the strictly convex part of the surface near the interface as a graph of a function z = f(r, t)and the non-convex part of the surface near the interface as a graph of a function z = φ(r), we show that if at time t = 0, g = 1n fn-1r vanishes linearly at the interface, the g(r; t) will become smooth up to the interface for long time before focusing.
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참고문헌 (23)
참고문헌 신청
B. Andrews / 1999 / Gauss curvature flow: The fate of the rolling stones / Invent. Math 138 (1) : 151 ~ 161
B. Chow / 1985 / Deforming convex hypersurfaces by the nth root of the Gaussian curvature / J. Differential Geom 22 (1) : 117 ~ 138
B. Chow / 1991 / On Harnack's inequality and entropy for the Gaussian curvature flow / Comm. Pure Appl. Math 44 (4) : 469 ~ 483
D. Chopp / 1999 / Waiting time effects for Gauss curvature flow / Indiana Univ. Math. J 48 (1) : 311 ~ 334
G. M. Lieberman / 1996 / Second Order Parabolic Differential Equations / World Scientific Pub- lishing Co., Inc
B. Chow / 1985 / Deforming convex hypersurfaces by the nth root of the Gaussian curvature / J. Differential Geom 22 (1) : 117 ~ 138
B. Chow / 1991 / On Harnack's inequality and entropy for the Gaussian curvature flow / Comm. Pure Appl. Math 44 (4) : 469 ~ 483
D. Chopp / 1999 / Waiting time effects for Gauss curvature flow / Indiana Univ. Math. J 48 (1) : 311 ~ 334
G. M. Lieberman / 1996 / Second Order Parabolic Differential Equations / World Scientific Pub- lishing Co., Inc
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