|COOKIES: By using this website you agree that we can place Google Analytics Cookies on your device for performance monitoring.|
Area minimizing surfaces in mean convex 3-manifolds
If you have a question about this talk, please contact Jonathan Ben-Artzi.
In this talk, we give several results on area minimizing surfaces in strictly mean convex 3-manifolds. First, we study the genus of absolutely area minimizing surfaces in a compact, orientable, strictly mean convex 3-manifold M bounded by a simple closed curve in the boundary of M. Our main result is that for any g>=0, the space of simple closed curves in the boundary of M where all the absolutely area minimizing surfaces they bound in M has genus >=g is open and dense in the space A of nullhomologous simple closed curves in the boundary of M. For showing this, we prove a bridge principle for absolutely area minimizing surfaces. Moreover, we show that for any g>=0, there exists a curve in A such that the minimum genus of the absolutely area minimizing surfaces it bounds is exactly g. As an application of these results, we further prove that the simple closed curves in the boundary of M bounding more than one minimal surface in M is an open and dense subset of A. We also show that there are disjoint simple closed curves in the boundary of M bounding minimal surfaces in M which are not disjoint. This allows us to answer a question of Meeks, by showing that for any strictly mean convex 3-manifold M, there exists a simple closed curve \Gamma in the boundary of M which bounds a stable minimal surface which is not embedded. This is a joint work with Theodora Bourni.
This talk is part of the Geometric Analysis and Partial Differential Equations seminar series.
This talk is included in these lists:
Note that ex-directory lists are not shown.
Other listsCambridge Public Policy Seminar Series Fluid Mechanics (DAMTP) Clare Hall
Other talksThe 4th Improving Immunohistochemistry Discussion Forum Duplicating the Human genome: The Origin Recognition Complex et al “Of Lambs and Hedgehogs” Software Innovation: Essence tba Transcriptional networks regulating blood vessels: Notch, Sox and arterial formation