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

D. Dominique Kemp

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.

https://www.ias.edu/video/introduction-decoupling-higher-dimensional-zero-curvature-hypersurfaces