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arXiv · 2211.06242

Spherical Minkowski content and natural parametrization on the sphere for Schramm-Loewner evolution

Tianyu Wei·Wanyang Dai
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Abstract

Studying SLE$_{\kappa}$ on $S^2$ provides a new and interesting perspective for the conformality of some 2-dimensional physical models. We prove the existence and some basic properties of the spherical Minkowski content of SLE$_{\kappa}$, which is finite and can be viewed as the natural parametrization of SLE$_{\kappa}$ on $S^2$.

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Tianyu Wei, Wanyang Dai. 2022-11-11. Spherical Minkowski content and natural parametrization on the sphere for Schramm-Loewner evolution. https://arxiv.org/abs/2211.06242

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