PreprintCC BY 4.0arXiv
Strongly linearly convex exhaustion of a class of ℂ-convex domains
Abstract
Let D⊆ ℂn be a bounded ℂ-convex domain with C1 boundary whose outward unit normal admits a modulus of continuity ω satisfying limt→ 0+ω(t)/√t. We prove that D admits an increasing exhaustion by bounded C∞ strongly linearly convex domains. This, in particular, answers a question posed by Azinberg \cite{azin} in affirmative for a class of domains D.
Related
- Small exponent Schatten class Toeplitz operators on convex domains of finite type
- W1,p error estimates of an IPDG and a class of HDG methods for the Poisson problem on convex polyhedral domains
- Silver Rate Is (Almost) Optimal for Gradient Descent: The Strongly Convex Case
- SLOPE DETERMINATION ON CONVEX DOMAINS: DIRICHLET DATA AND CRANDALL-PAZY DIRECTIONS
- On strongly convex Kähler--Berwald manifolds
BibTeX
@misc{gupta2026strongly,
title = {{Strongly linearly convex exhaustion of a class of $\mathbbC$-convex domains}},
author = {Naveen Gupta},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.35474},
eprint = {2609.35474},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.35474},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Strongly linearly convex exhaustion of a class of ℂ-convex domains
AU - Naveen Gupta
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.35474
UR - https://arxiv.org/abs/2609.35474
AB - Let D⊆ ℂ^n be a bounded ℂ-convex domain with C^1 boundary whose outward unit normal admits a modulus of continuity ω satisfying lim_t→ 0^+ω(t)/√t. We prove that D admits an increasing exhaustion by bounded C^∞ strongly linearly convex domains. This, in particular, answers a question posed by Azinberg \cite{azin} in affirmative for a class of domains D.
ER -