@article{00f9e286e1a84dfa953438ae4120d642,
title = "Function Theory and Holomorphic Maps on Symmetric Products of Planar Domains",
abstract = "We show that the (Formula presented.)-problem is globally regular on a domain in (Formula presented.), which is the n-fold symmetric product of a smoothly bounded planar domain. Remmert–Stein type theorems are proved for proper holomorphic maps between equidimensional symmetric products and proper holomorphic maps from Cartesian products to symmetric products. It is shown that proper holomorphic maps between equidimensional symmetric products of smooth planar domains are smooth up to the boundary.",
keywords = "Boundary regularity, Dbar-problem, Non-Lipschitz domains, Proper maps, Symmetric products",
author = "Debraj Chakrabarti and Sushil Gorai",
note = "Funding Information: We would like to thank W{\l}odzimierz Zwonek and Armen Edigarian for helpful information and {\L}ukasz Kosi{\'n}ski for telling us about his result on the boundary geometry of the symmetrized bidisc (Lemma 5.4 below). Debraj Chakrabarti would like to thank Diganta Borah for his invitation to visit IISER Pune, and colleagues there for useful comments and discussions on the subject of this paper. Sushil Gorai would like to thank Stat–Math Unit, Indian Statistical Institute, Bengaluru Centre for providing a congenial atmosphere for research. We would also like to express our special gratitude to the Dean of TIFR-CAM, Bengaluru, Prof. Mythily Ramaswamy for facilitating our collaboration. Without her support (including the provision of chauffeured cars for travel in Bengaluru) this paper would never have been written. Sushil Gorai was supported by an INSPIRE Faculty Fellowship awarded by DST, Government of India. Publisher Copyright: {\textcopyright} 2014, Mathematica Josephina, Inc.",
year = "2015",
month = oct,
day = "1",
doi = "10.1007/s12220-014-9509-y",
language = "English",
volume = "25",
pages = "2196--2225",
journal = "Journal of Geometric Analysis",
issn = "1050-6926",
publisher = "JOURNAL OF GEOMETRIC ANALYSIS",
number = "4",
}