Cones, rectifiability and singular integral operators.

Abstract: Let K(x, V, s) be the open cone centred at x, with direction V, and aperture s. It is easy to see that if a set E satisfies for some V and s the condition: "if x belongs to E, then E has an empty intersection with K(x, V, s)", then E is a subset of a Lipschitz graph. To what extent can we weaken the condition above and still get meaningful information about the geometry of E? It depends on what we mean by "meaningful information'', of course. For example, one could ask for rectifiability of E, or if E contains big pieces of Lipschitz graphs, or if nice singular integral operators are bounded in L^2(E). In the talk I will discuss these three closely related questions.

analysis of PDEsclassical analysis and ODEs

Audience: researchers in the topic

HA-GMT-PDE Seminar

Series comments: Description: A senior graduate student/postdoc series in harmonic analysis, geometric measure theory, and partial differential equations.

Meetings will be weekly, and usually will occur on Monday, with some exceptions. For each talk, the Zoom link is made available in the website too. Contact Bruno Poggi at poggi008@umn.edu if you would like to subscribe to the seminar mailing list.