Veranstaltungen

06. März 2025, 15:00 bis 17:00

AKOR Seminar: On the semialgebraic Whitney extension problem

Andere

Armin Rainer, TU Wien

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.

 

Kalendereintrag

Veranstaltungsort

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

 

Veranstalter

VADOR
vador@tuwien.ac.at

 

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