Petty projection inequality on the sphere and on the hyperbolic space

Y. Lin; Y. Wu

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arXiv · 2406.13428

Petty projection inequality on the sphere and on the hyperbolic space

Y. Lin·Y. Wu

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Abstract

Using gnomonic projection and Poincar\'e model, we first define the spherical projection body and hyperbolic projection body in spherical space $\mathbb{S}^n$ and hyperbolic space $\mathbb{H}^n$, then define the spherical Steiner symmetrization and hyperbolic Steiner symmetrization, finally prove the spherical projection inequality and hyperbolic projection inequality.

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Y. Lin, Y. Wu. 2024-06-19. Petty projection inequality on the sphere and on the hyperbolic space. https://arxiv.org/abs/2406.13428

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