Remarks on a class of solutions to the minimal surface system

Wang, Mu-Tao

doi:10.1090/conm/367/06758

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“…In 1914, Bernstein proved that the only entire minimal graph in R 3 is a plane. This result was generalized to R m+1 for m ≤ 7, and higher dimensions and codimensions under various growth conditions, see [EH], [SXW], [Wa3] and their references. In 1965, Chern [Ch] showed that the only entire graphic hypersurface in R m+1 with constant mean curvature must be minimal.…”

Section: Introductionmentioning

confidence: 99%

Bernstein theorems for space-like graphs with parallel mean curvature and controlled growth

2008

Journal of Geometry and Physics

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Section: Introductionmentioning

confidence: 99%

Bernstein theorems for space-like graphs with parallel mean curvature and controlled growth

2008

Journal of Geometry and Physics

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Curvature decay estimates of graphical mean curvature flow in higher codimensions

Smoczyk

Tsui

Wang

2016

Trans. Amer. Math. Soc.

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Abstract. We derive pointwise curvature estimates for graphical mean curvature flows in higher codimensions for a flat ambient space. To the best of our knowledge, this is the first such estimates without assuming smallness of first derivatives of the defining map. An immediate application is a convergence theorem of the mean curvature flow of the graph of an area decreasing map between flat Riemann surfaces.

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Remarks on a class of solutions to the minimal surface system

Cited by 2 publications

References 31 publications

Bernstein theorems for space-like graphs with parallel mean curvature and controlled growth

Bernstein theorems for space-like graphs with parallel mean curvature and controlled growth

Curvature decay estimates of graphical mean curvature flow in higher codimensions

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