| Abstract: |
| We present Hardy inequalities on the Heisenberg group in a form reminiscent of Davies' inequalities in the Euclidean setting. Our results have two notable features. First, they improve previously known inequalities, yielding sharper estimates. Second, we prove them without imposing any boundary regularity assumptions. We also discuss how these Davies-type Hardy inequalities can be converted into sub-Laplacian eigenvalue lower bounds. This talk is based on recent joint work with Rupert L. Frank (LMU Munich and Caltech) and Ari Laptev (Imperial College London). |
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