Date/Time
Date(s) - 31/10/2025
1:30 pm - 2:30 pm

Location: Hybrid HH 410 and https://mcmaster.zoom.us/j/2601491351

Speaker: CARLOS MUDARRA (NTNU)

Title: Smooth convex extensions and applications

 

Abstract: The Whitney extension theorem determines whether a jet (a function along with certain putative derivatives) on a subset of R^n admits an extension of a given order of smoothness to the whole space. What optimal conditions on those jets would guarantee the existence of smooth extensions that are convex as well? We give answer to this question for various Banach spaces and orders of smoothness. Also, our methods allow us to obtain improved versions of the original Whitney’s theorem for arbitrary functions that are valid in infinite-dimensional settings. As a corollary, we obtain the Kirszbraun’s extension theorem for Lipschitz mappings via simple and explicit formulas. Based on joint work with Daniel Azagra and Erwan Le Gruyer.