Advertisement

Archiv der Mathematik

, Volume 71, Issue 1, pp 63–70 | Cite as

Heat operator and $ \zeta $-function estimates for surfaces

  • Christian Bär

Abstract.

Using Kato's comparison principle for heat semi-groups we derive estimates for the trace of the heat operator on surfaces with variable curvature. This estimate is from above for positively curved surfaces of genus 0 and from below for genus g ≥ 2. It is shown that the estimates are asymptotically sharp for small time and in the case of positive curvature also for large time. As a consequence we can estimate the corresponding \( \zeta \)-function by the Riemann \( \zeta \)-function.

Keywords

Kato Large Time Function Estimate Small Time Curve Surface 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Birkhäuser Verlag, Basel 1998

Authors and Affiliations

  • Christian Bär
    • 1
  1. 1.Mathematisches Institut, Universität Freiburg, Eckerstraße 1, D-79104 Freiburg, GermanyDE

Personalised recommendations