Curvature estimates for graphs with prescribed mean curvature and flat normal bundle

Abstract

We consider graphs Σ n ⊂ R m with prescribed mean curvature and flat normal bundle.

Curvature estimates for submanifolds with prescribed Gauss image and mean curvature

“…In author's previous work, Schoen-Simons-Yau type curvature estimates [10] and Ecker-Huisken type curvature estimates [1] have be generalized to the flat normal bundle situation [14] [12]. Using some techniques in [2], Fröhlich-Winklmann [3] derived interior curvature estimates for the flat normal bundle case and generalized our results in [12].…”

“…From L p −estimates to pointwise estimates we need the following mean value inequality in [3]: Lemma 5.1. Let S be an n−graph in R m+n .…”

“…In the final section we prove our main results. It is done by using L p −curvature estimates in §4 and mean value inequality of Fröhlich-Winklman in [3].…”

Lectures on normal Coulomb frames in the normal bundle of twodimensional immersionen of higher codimension

“…A curvature estimate for surface graphs of prescribed mean curvature and theorems of Bernstein type for minimal graphs can be found for example in Bergner and Fröhlich [4]. Curvature estimates resting upon methods of Schoen, Simon, Yau [47] and Ecker, Huisken [24], [25] can be found in Wang [55], [56], Fröhlich and Winklmann [31], or Xin [60].…”