Exposing maps in strictly pseudoconvex domains with smooth dependence on parameters

Lewandowski, Arkadiusz

doi:10.1090/proc/15669

Exposing maps in strictly pseudoconvex domains with smooth dependence on parameters
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by Arkadiusz Lewandowski

Proc. Amer. Math. Soc. 149 (2021), 4881-4889

DOI: https://doi.org/10.1090/proc/15669

Published electronically: August 12, 2021

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Abstract:

We prove that given a family $(G_t)$ of strictly pseudoconvex domains varying in a $\mathcal {C}^k$-continuous way with respect to the topology on domains (with $k\geq 2$), there exists a $\mathcal {C}^{\lfloor {\frac {k-1}{2}}\rfloor }$-continuously varying family of exposing maps $h_{t,\zeta }$ for all $G_t$ at every $\zeta \in \partial G_t.$

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