Entire graphs under a general flow

• Autorzy: Mao, J. , Li, G. , Wu, C.
• Języki publikacji: EN

Abstrakty

EN

An initial entire graph with bounded second fundamental form in Rn+1 over some hyperplane is evolving under a general flow defined in the paper. For an additionally suitable condition in the main theorem, we obtain gradient and curvature estimates, leading to long-time existence of the flow, and convergence to an entire graph in the limit.

Słowa kluczowe

PL

równanie pierwiastkowe; krzywizna; średnia krzywizny

EN

evolution equation; mean curvature; entire graph

• Czasopismo: Demonstratio Mathematica
• Rocznik: 2009
• Tom: Vol. 42, nr 3
• Strony: 631-640
• Opis fizyczny: Bibliogr. 4 poz.

Twórcy

autor

Mao, J.

autor

Li, G.

autor

Wu, C.

• School of Mathematics and Computer Science Hubei University Wuhan 430062, People's Republic of China,

Bibliografia

• [1] G. Huisken, Flow by the mean curvature of convex surfaces into spheres, J. Differential Geom. 20 (1984), 237-266.
• [2] G. Huisken, The volume preserving mean curvature flow, J. Reine Angew. Math. 382 (1987), 35-48.
• [3] K. Ecker, G. Huisken, Mean curvature evolution of entire graphs, Ann. of Math. 130 (1989), 453-471.
• [4] Xi-ping Zhu, Lectures on mean curvature flow, AMS/IP Studies in Advanced Mathematics, vol. 32. American Mathematical Society. International Press, Providence (2002).