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Analysis Seminar

Thursday, November 17, 2022 - 3:30pm

Dóminique Kemp



University of Pennsylvania



The ruled hypersurfaces are distinguished by being comprised of lines. When this characteristic exists as a consequence of vanishing principal curvatures, it yields possibilities for comparison with cylinders extending over lower-dimensional surfaces. In this way, the decoupling for the cone was  secured by Bourgain-Demeter, and the decoupling for tangent developable surfaces in \R^3 not too long after. In this talk, we show how the analysis executed there may be generalized to the higher-dimensional analogues of the tangent developables.