Abstract
In this paper, we give two results concerning the positivity property of the Paneitz operator- a fourth order conformally covariant elliptic operator. We prove that the Paneitz operator is positive for a compact Riemannian manifold without boundary of dimension at least six if it has positve scalar curvature as well as nonnegative Q-curvature. We also show that the positivity of the Paneitz operator is preserved in dimensions greater than four in taking a connected sum.
Original language | English (US) |
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Pages (from-to) | 329-342 |
Number of pages | 14 |
Journal | Discrete and Continuous Dynamical Systems |
Volume | 7 |
Issue number | 2 |
DOIs | |
State | Published - 2001 |
Externally published | Yes |
All Science Journal Classification (ASJC) codes
- Analysis
- Discrete Mathematics and Combinatorics
- Applied Mathematics
Keywords
- Connected Sum
- Eigenvalues
- Paneitz Opertaor