2005/05/12 by L. Baracco, Baracco, L., D. Zaitsev +3 · 1 citation
Mathematics · #32H02 #32H12 #Complex Variables (math.CV) #FOS: Mathematics #math.CV #msc:32H02 #msc:32H12
paper · pdf · doi:10.48550/arxiv.math/0505264
13 pages
arxiv created 2005/05/12 · arxiv updated 2009/12/01
The goal of this paper is twofold. First, to give purely local boundary uniqueness results for maps defined only on one side as germs at a boundary point and hence not necessarily sending any domain to itself and also under the weaker assumption that f(z)=z+o(|z-p|3) holds only for z in a proper cone in D with vertex p. Such results have no analogues in one complex variable in contrast to the situation when a domain is preserved. And second, to extend the above results from boundaries of domains to submanifolds of higher codimension.