Catlin's Global Regularity - A New Proof and Generalizations
Explore a groundbreaking alternative proof of Catlin's global regularity theorem in this 58-minute lecture from the Workshop on "Analysis and Geometry in Several Complex Variables" at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into the concept of "tower multi-type," a more general intrinsic geometric condition than finite type, and its implications for boundary stratification. Discover how this new approach leads to Catlin's potential-theoretic "Property (P)" and subsequently to global regularity via compactness estimates. Examine notable applications, including Bell and Ligocka's Condition R and its impact on boundary smoothness of proper holomorphic maps, extending Fefferman's renowned theorem. Gain insights into this complex mathematical topic, bridging local algebraic and analytic geometric invariants with equation estimates through potential theory.