Under the extra assumption that the lowest eigenvalue is differentiable along time, we derive an explicit formula for the evolution of the lowest eigenvalue of the Laplace-Beltrami operator with potential in the abstract setting.
We then derive explicit formula for the evolution equation of the lowest eigenvalue of the Laplace-Beltrami operator with potential in the abstract setting. The lowest eigenvalue is monotone under the same technical assumption. In particular the lowest eigenvalue is nondecreasing in the above mentioned geometric flows.
The PDF of the paper is available here:
Hongxin Guo | guo@wzu.edu.cn |
Robert Philipowski | robert.philipowski@uni.lu |
Anton Thalmaier | anton.thalmaier@uni.lu |