Events

24. April 2025, 16:00 until 17:00

AKOR Seminar: On the semialgebraic Whitney extension problem

Seminar

Armin Rainer, TU Wien

(Postponed from 06.03.2025)

In 1934, Whitney raised the question of how one can decide whether a function defined on a closed subset of real n-space is the restriction of a $C^m$ function on real n-space. He gave a characterization in dimension 1. The problem was fully solved by Fefferman in 2006.

In this talk, I will discuss a related conjecture: if a semialgebraic function on a closed subset of real n-space has a $C^m$ extension, then it has a semialgebraic $C^m$ extension. In particular, I will show that the $C^{1,\omega}$ case of the conjecture is true in a uniformly bounded way, for each semialgebraic modulus of continuity $\omega$. 

The proof is based on the existence of semialgebraic Lipschitz selections for certain affine-set valued maps and on a uniform semialgebraic version of Whitney’s extension theorem. This is joint work with Adam Parusinski.

 

Calendar entry

Event location

Sem. R. DB gelb 04
1040 Wien
Wiedner Hauptstraße 8 E105-4

 

Organiser

VADOR
vador@tuwien.ac.at

 

Public

No

 

Entrance fee

No

 

Registration required

No