Mean curvature self-shrinkers of high genus: Non-compact examples
Mean curvature self-shrinkers of high genus: Non-compact examples
Abstract We give the first rigorous construction of complete, embedded self-shrinking hypersurfaces under mean curvature flow, since Angenent’s torus in 1989. The surfaces exist for any sufficiently large prescribed genus g , and are non-compact with one end. Each has <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mrow> <m:mn>4</m:mn> <m:mo></m:mo> <m:mi>g</m:mi> </m:mrow> <m:mo>+</m:mo> <m:mn>4</m:mn> …