Abstract
Given a compact Riemannian manifold with umbilic boundary, we prove the existence of conformally related metrics of zero scalar curvature and constant mean curvature on the boundary, under suitable hypotheses on the Weyl tensor. In order to carry out the estimates on the Sobolev quotient, we also prove the existence of conformal Fermi coordinates.
Original language | English (US) |
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Pages (from-to) | 1599-1620 |
Number of pages | 22 |
Journal | Indiana University Mathematics Journal |
Volume | 54 |
Issue number | 6 |
DOIs | |
State | Published - Jan 1 2005 |
Externally published | Yes |
All Science Journal Classification (ASJC) codes
- Mathematics(all)