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

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.



Indiana University; Member, School of Mathematics