Abstract
We develop heat kernel and Green's function estimates for manifolds with positive bottom spectrum. The results are then used to establish existence and sharp estimates of the solution to the Poisson equation on such manifolds with Ricci curvature bounded below. As an application, we show that the curvature of a steady gradient Ricci soliton must decay exponentially if it decays faster than linear and the potential function is bounded above.
Original language | English (US) |
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Pages (from-to) | 81-145 |
Number of pages | 65 |
Journal | Advances in Mathematics |
Volume | 348 |
DOIs | |
State | Published - May 25 2019 |
Bibliographical note
Publisher Copyright:© 2019 Elsevier Inc.
Keywords
- Bottom spectrum
- Green's function
- Poisson equation
- Steady Ricci solitons