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A Metric Deformation to Obtain a Positive/Negative Gaussian Curvature on a Disk

  • Hajime Kawakami
Published/Copyright: March 10, 2010
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Georgian Mathematical Journal
From the journal Volume 15 Issue 1

Abstract

We conjecture that the Gauss–Bonnet formula gives a necessary and sufficient condition for the existence of a metric deformation to obtain a positive/negative Gaussian curvature on a disk. The conjecture is reduced to a problem of a partial differential inequality with Dirichlet–Neumann boundary condition. We give a partial answer and an example.

Received: 2006-06-08
Published Online: 2010-03-10
Published in Print: 2008-March

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