# Heat Operator and Zeta-Function Estimates for Surfaces

#### Autoren: Christian Bär (1998)

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 $g \ge 2$. 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.

Zeitschrift:
Arch. Math.
Verlag:
Springer
Seiten:
63-70
Band:
71, no. 1

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