Convexity estimates for high codimension mean curvature flow
Convexity estimates for high codimension mean curvature flow
Abstract We consider the flow by mean curvature of smooth n -dimensional submanifolds of $${\mathbb {R}}^{n+k}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>+</mml:mo> <mml:mi>k</mml:mi> </mml:mrow> </mml:msup> </mml:math> , $$k \ge 2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>k</mml:mi> <mml:mo>≥</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> , which are compact and quadratically pinched. We establish …