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arXiv · 2207.09886

Qualitative Properties of Singular Solutions to the Fractional Yamabe Problem

Sergio Cruz-Blázquez·Azahara DelaTorre·David Ruiz
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Abstract

In this paper we are interested in the qualitative properties of the solutions to the fractional Yamabe problem in $\mathbb{R}^n$ which present an isolated singularity. In particular, we prove that the Morse index of any such solution is infinity. The proof uses a Emden Fowler type transformation, so that we can pass to a nonlocal 1D problem posed in $\mathbb{R}$.

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Sergio Cruz-Blázquez, Azahara DelaTorre, David Ruiz. 2022-07-20. Qualitative Properties of Singular Solutions to the Fractional Yamabe Problem. https://arxiv.org/abs/2207.09886

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