Showing papers in "Duke Mathematical Journal in 1977"

Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations

Abstract: A simple duality argument shows these two problems are completely equivalent ifp and q are dual indices, (]/) + (I/q) ]. ]nteresl in Problem A when S is a sphere stems from the work of C. Fefferman [3], and in this case the answer is known (see [l I]). Interest in Problem B was recently signalled by 1. Segal [6] who studied the special case S {(x, y) yZ xz I} and gave the interpretation of the answer as a space-time decay for solutions of the Klein-Gordon equation with finite relativistic-invariant norm. In this paper we give a complete solution when S is a quadratic surface given by

Totally geodesic submanifolds of symmetric spaces, I

Abstract: One purpose of this article is to establish a general method to determine stability of totally geodesic submanifolds of symmetric spaces. The method is used to determine the stability of the basic totally geodesic submanifolds M+,M introduced and studied by Chen and Nagano in (Totally geodesic submanifolds of symmetric spaces, II, Duke Math. J. 45 (1978), 405-425) as minimal submanifolds. The other purpose is to establish a stability theorem for minimal totally real sub- manifolds of Kahlerian manifolds.