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Petty projection inequality on the sphere and on the hyperbolic space (2406.13428v1)
Published 19 Jun 2024 in math.MG
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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