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- W2015373073 abstract "We determine all proper holomorphic maps of balls $${mathbb {B}}_2 rightarrow {mathbb {B}}_3$$ admitting a $$C^3$$ extension up to the boundary of $${mathbb {B}}_2$$ and whose boundary values $$S^3 rightarrow S^5$$ are subelliptic harmonic maps (in the sense of Jost and Xu in Trans Am Math Soc 350(11):4633–4649, 1998). A new numerical CR invariant, the CR degree of a CR map of spheres $$S^{2n+1} rightarrow S^{2N+1}$$ , is introduced and used to distinguish among the spherical equivalence classes in Faran’s list $$P^*(2,3)$$ (cf. Faran in Invent Math 68:441–475, 1982). As an application, the boundary values $$phi $$ of Alexander’s map $$Phi in P(2,3)$$ (cf. Alexander in Indiana Univ Math J 26:137–146, 1977) is shown to be homotopically nontrivial, as a map of $${ (z,w) in S^3 : w + overline{w} > 0 }$$ into $$S^5 {setminus } S^3$$ ." @default.
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- W2015373073 date "2014-06-04" @default.
- W2015373073 modified "2023-10-06" @default.
- W2015373073 title "Proper holomorphic maps in harmonic map theory" @default.
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- W2015373073 doi "https://doi.org/10.1007/s10231-014-0429-z" @default.
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