| 1. |
- Lind, Andreas, 1979-
(författare)
-
Holomorphic automorphisms of Danielewski surfaces
- 2009
-
Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- In this thesis we define the notion of an overshear on a Danielewskisurface. Next we show that the group generated by the overshears is dense in the component of the identity of the automorphism group. Moreover, we show that the overshear group has a structure of an amalgamated product, and as consequence of this the overshear group is a proper subgroup of the automorphism group. Finally we classify the R^n-actions, and therefore the one parameter subgroups, of the overshear group. We also show that any Lie subgroup of an amalgamated product can be conjugated to one of the factors of the amalgamated product.
|
|
| 2. |
- Lodin, Sam
(författare)
-
Holomorphic embeddings and applications
- 2009
-
Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- In the first part of this thesis we consider the question of the number of equivalenceclasses of holomorphic embeddings of Ck into Cn. We show the existence of holomorphicfamilies of proper holomorphic embeddings of Ck into Cn (0 < k < n−1),such that members of the family are pairwise nonequivalent in a suitable sense. Asan application we use these embeddings to deduce results in the theory of holomorphictransformation groups.In the second part of the thesis the question of plurisubharmonic extension is connectedto analytic discs, i.e. nonconstant holomorphic maps of the unit disc in Cinto Cn. We derive results on plurisubharmonic extension for analytic polyhedra.
|
|
| 3. |
- Andrist B., Rafael, et al.
(författare)
-
Holomorphic Automorphisms of Danielewski Surfaces II: Structure of the Overshear Group
- 2015
-
Ingår i: Journal of Geometric Analysis. - : Springer Science and Business Media LLC. - 1050-6926 .- 1559-002X. ; 25:3, s. 1859-1889
-
Tidskriftsartikel (refereegranskat)abstract
- We apply Nevanlinna theory for algebraic varieties to Danielewski surfaces and investigate their group of holomorphic automorphisms. Our main result states that the overshear group, which is known to be dense in the identity component of the holomorphic automorphism group, is a free product.
|
|
| 4. |
- Borell, Stefan, et al.
(författare)
-
Embeddings through Discrete Sets of Discs
- 2008
-
Ingår i: Arkiv för matematik. - : International Press of Boston. - 0004-2080 .- 1871-2487. ; 46:2, s. 251-269
-
Tidskriftsartikel (refereegranskat)abstract
- We investigate whether a Stein manifold M which allows proper holomorphic embedding into ℂ n can be embedded in such a way that the image contains a given discrete set of points and in addition follow arbitrarily close to prescribed tangent directions in a neighbourhood of the discrete set. The infinitesimal version was proven by Forstnerič to be always possible. We give a general positive answer if the dimension of M is smaller than n/2 and construct counterexamples for all other dimensional relations. The obstruction we use in these examples is a certain hyperbolicity condition.
|
|
| 5. |
- Borell, Stefan, et al.
(författare)
-
Non-equivalent embeddings into complex Euclidean spaces
- 2006
-
Ingår i: International Journal of Mathematics. - 0129-167X. ; 17:9, s. 1033-1046
-
Tidskriftsartikel (refereegranskat)abstract
- We study the number of equivalence classes of proper holomorphic embeddings of a Stein space X into C-n. In this paper we prove that if the automorphism. group of X is a Lie group and there exists a proper holomorphic embedding of X into C-n, 0 < dim X < n, then for any k >= 0 there exist uncountably many non-equivalent proper holomorphic embeddings Φ: X x C-k hooked right arrow C-n x C-k. For k = 0 all embeddings will be proved to satisfy the additional property of C-n\Φ)(X) being (n-dim X)-Eisenman hyperbolic. As a corollary we conclude that there are uncountably many non-equivalent proper holomorphic embeddings of C-k into C-n whenever 0 < k < n.
|
|
| 6. |
|
|
| 7. |
|
|
| 8. |
- Ekholm, Tobias, et al.
(författare)
-
Total curvature and area of curves with cusps and of surface maps.
- 2005
-
Ingår i: Mathematica Scandinavica. - 0025-5521 .- 1903-1807. ; 96:2, s. 224-242
-
Tidskriftsartikel (refereegranskat)abstract
- A curvature-area inequality for planar curves with cusps is derived. Using this inequality, the total (Lipschitz-Killing) curvature of a map with stable singularities of a closed surface into the plane is shown to be bounded below by the area of the map divided by the square of the radius of the smallest ball containing the image of the map. This latter result fills the gap in Santalo's [7] proof of a similar estimate for surface maps into R-n, n > 2.
|
|
| 9. |
|
|
| 10. |
- Forstneric, Franc, et al.
(författare)
-
An interpolation theorem for proper holomorphic embeddings
- 2005
-
Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Given a Stein manifold X of dimension n>1, a discrete sequence a_j in X, and a discrete sequence b_j in C^m where m > [3n/2], there exists a proper holomorphic embedding of X into C^m which sends a_j to b_j for every j=1,2,.... This is the interpolation version of the embedding theorem due to Eliashberg, Gromov and Schurmann. The dimension m cannot be lowered in general due to an example of Forster.
|
|
