| Abstract: |
| I will describe some recent work on locally constrained inverse curvature flows for hypersurfaces and their applications in proving geometric inequalities. These flows were first introduced by Brendle-Guan-Li in the case of space forms and were recently extended to cases with boundaries. The flow speed involves higher-order mean curvature and includes a local term designed to preserve certain natural geometric quantities, such as quermassintegrals. We show that the flow has a natural monotonicity property, preserves some convexity, and exhibits long-time existence and convergence. These results can be applied to establish isoperimetric-type geometric inequalities for hypersurfaces. |
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