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arXiv · 2104.01979

The spectrum of the Laplacian and volume growth of proper minimal submanifolds

G. Pacelli Bessa·Vicent Gimeno·Panagiotis Polymerakis
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Abstract

We give upper bounds for the bottom of the essential spectrum of properly immersed minimal submanifolds of $\mathbb{R}^{n}$ in terms of their volume growth. Our result improves the extrinsic version of Brook's essential spectrum estimate given by Ilias-Nelli-Soret in \cite[Cor.3]{ins}.

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G. Pacelli Bessa, Vicent Gimeno, Panagiotis Polymerakis. 2021-04-05. The spectrum of the Laplacian and volume growth of proper minimal submanifolds. https://arxiv.org/abs/2104.01979

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