Kakeya sets of curves
نویسنده
چکیده
In this paper we investigate an analogue for curves of the famous Kakeya conjecture about straight lines. The simplest version of the latter asks whether a set in R that includes a unit line segment in every direction must necessarily have dimension n. The analogue we have in mind replaces the line segments by curved arcs from a specified family. (This is a quite different problem from that considered by Minicozzi and Sogge [18] who looked at geodesics in curved space.) The families of curves we are interested in arise from Hörmander’s conjecture in harmonic analysis, which deals with oscillatory integral operators of the form
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