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Proper holomorphic maps in harmonic map theory
We determine all proper holomorphic maps of balls B 2 → B 3 admitting a C 3 extension up to the boundary of B 2 and whose boundary values S 3 → 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...
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| Published in: | Annali di matematica pura ed applicata 2015-10, Vol.194 (5), p.1469-1498 |
|---|---|
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Subjects: | |
| Citations: | Items that this one cites Items that cite this one |
| Online Access: | Get full text |
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| Summary: | We determine all proper holomorphic maps of balls
B
2
→
B
3
admitting a
C
3
extension up to the boundary of
B
2
and whose boundary values
S
3
→
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
2
n
+
1
→
S
2
N
+
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
ϕ
of Alexander’s map
Φ
∈
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
)
∈
S
3
:
w
+
w
¯
>
0
}
into
S
5
\
S
3
. |
|---|---|
| ISSN: | 0373-3114 1618-1891 |
| DOI: | 10.1007/s10231-014-0429-z |