Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
  1. Home
  2. Search

Refine search

Refine search

Access:
Content type:
Publication date:
Apply   From and To filters
Subject: Show more
Journals Show more
Publishers: Show more
Societies Show more
Series: Show more
Collections: Show more

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Save to Kindle
  • Save to Dropbox
  • Save to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
Cancel
×

2 results

  • EFFECTIVE ISOMETRIC EMBEDDINGS FOR CERTAIN HERMITIAN HOLOMORPHIC LINE BUNDLES

  • WING-KEUNG TO, SAI-KEE YEUNG
  • Journal:
    Journal of the London Mathematical Society / Volume 73 / Issue 3 / June 2006
    Published online by Cambridge University Press:
    16 June 2006, pp. 607-624
    Print publication:
    June 2006

  • We consider bihomogeneous polynomials on complex Euclidean spaces that are positive outside the origin and obtain effective estimates on certain modifications needed to turn them into squares of norms of vector-valued polynomials on complex Euclidean space. The corresponding results for hypersurfaces in complex Euclidean spaces are also proved. The results can be considered as Hermitian analogues of Hilbert's seventeenth problem on representing a positive definite quadratic form on $\mathbb{R}^n$ as a sum of squares of rational functions. They can also be regarded as effective estimates on the power of a Hermitian line bundle required for isometric projective embedding. Further applications are discussed.

  • Proper Holomorphic self-maps of quasi-circular domains in C2

  • B. Coupet, Y. Pan, A. Sukhov
  • Journal:
    Nagoya Mathematical Journal / Volume 164 / December 2001
    Published online by Cambridge University Press:
    22 January 2016, pp. 1-16
    Print publication:
    December 2001
    • Article
      • You have access
    • PDF
    • Export citation

  • In this paper, we prove that every proper holomorphic self-map of a smoothly bounded pseudoconvex circular or Hartogs domain of finite type in C2 is biholomorphic.