Videos

An Introduction to the Decoupling of Higher Dimensional, Zero Curvature Hypersurfaces

Presenter
December 7, 2022
Abstract
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 R3 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.