Perelman's $\lambda$-functional on manifolds with conical singularities

Xianzhe Dai; Changliang Wang

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arXiv · 1708.03937

Perelman's $\lambda$-functional on manifolds with conical singularities

Xianzhe Dai·Changliang Wang

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Abstract

In this paper, we prove that on a compact manifold with isolated conical singularity the spectrum of the Schr\"odinger operator $-4\Delta+R$ consists of discrete eigenvalues with finite multiplicities, if the scalar curvature $R$ satisfies a certain condition near the singularity. Moreover, we obtain an asymptotic behavior for eigenfunctions near the singularity. As a consequence of these spectral properties, we extend the theory of the Perelman's $\lambda$-functional on smooth compact manifolds to compact manifolds with isolated conical singularities.

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BibTeX RIS

Xianzhe Dai, Changliang Wang. 2017-08-13. Perelman's $\lambda$-functional on manifolds with conical singularities. https://arxiv.org/abs/1708.03937

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