On local geometry of finite multitype hypersurfaces

Martin Kolář

Archivum Mathematicum (2007)

  • Volume: 043, Issue: 5, page 459-466
  • ISSN: 0044-8753

Abstract

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This paper studies local geometry of hypersurfaces of finite multitype. Catlin’s definition of multitype is applied to a general smooth hypersurface in ℂ n + 1 . We prove biholomorphic equivalence of models in dimension three and describe all biholomorphisms between such models. A finite constructive algorithm for computing multitype is described. Analogous results for decoupled hypersurfaces are given.

How to cite

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Kolář, Martin. "On local geometry of finite multitype hypersurfaces." Archivum Mathematicum 043.5 (2007): 459-466. <http://eudml.org/doc/250169>.

@article{Kolář2007,
abstract = {This paper studies local geometry of hypersurfaces of finite multitype. Catlin’s definition of multitype is applied to a general smooth hypersurface in $\mathbb \{C\}^\{n+1\}$. We prove biholomorphic equivalence of models in dimension three and describe all biholomorphisms between such models. A finite constructive algorithm for computing multitype is described. Analogous results for decoupled hypersurfaces are given.},
author = {Kolář, Martin},
journal = {Archivum Mathematicum},
keywords = {finite type; Catlin’s multitype; model hypersurfaces; biholomorphic equivalence; decoupled domains; finite type; Catlin's multitype; model hypersurfaces; biholomorphic equivalence; decoupled domains},
language = {eng},
number = {5},
pages = {459-466},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {On local geometry of finite multitype hypersurfaces},
url = {http://eudml.org/doc/250169},
volume = {043},
year = {2007},
}

TY - JOUR
AU - Kolář, Martin
TI - On local geometry of finite multitype hypersurfaces
JO - Archivum Mathematicum
PY - 2007
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 043
IS - 5
SP - 459
EP - 466
AB - This paper studies local geometry of hypersurfaces of finite multitype. Catlin’s definition of multitype is applied to a general smooth hypersurface in $\mathbb {C}^{n+1}$. We prove biholomorphic equivalence of models in dimension three and describe all biholomorphisms between such models. A finite constructive algorithm for computing multitype is described. Analogous results for decoupled hypersurfaces are given.
LA - eng
KW - finite type; Catlin’s multitype; model hypersurfaces; biholomorphic equivalence; decoupled domains; finite type; Catlin's multitype; model hypersurfaces; biholomorphic equivalence; decoupled domains
UR - http://eudml.org/doc/250169
ER -

References

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  11. Kolář M., Convexifiability and supporting functions in ℂ 2 , Math. Res. Lett. 2 (1995), 505–513. (1995) MR1355711
  12. Kolář M., Generalized models and local invariants of Kohn Nirenberg domains, to appear in Math. Z. Zbl1137.32014MR2390081
  13. Kolář M., On local convexifiability of type four domains in ℂ 2 , Differential Geometry and Applications, Proceeding of Satellite Conference of ICM in Berlin 1999, 361–371. (1999) MR1708924
  14. Kolář M., Necessary conditions for local convexifiability of pseudoconvex domains in ℂ 2 , Rend. Circ. Mat. Palermo 69 (2002), 109–116. MR1972429
  15. Kolář M., Normal forms for hypersurfaces of finite type in ℂ 2 , Math. Res. Lett. 12 (2005), 523–542. 
  16. Nikolov N., Biholomorphy of the model domains at a semiregular boundary point, C.R. Acad. Bulgare Sci. 55 (2002), no. 5, 5–8. Zbl1010.32018MR1938822
  17. Yu J., Peak functions on weakly pseudoconvex domains, Indiana Univ. Math. J. 43 (1994), no. 4, 1271–1295. (1994) Zbl0828.32003MR1322619

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