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We introduce a new geometric invariant called the obtuse constant of spaces with curvature bounded below. We first find relations between this invariant and the normalized volume. We also discuss… Click to show full abstract
We introduce a new geometric invariant called the obtuse constant of spaces with curvature bounded below. We first find relations between this invariant and the normalized volume. We also discuss the case of maximal obtuse constant equal to $\pi/2$, where we prove some rigidity for spaces. Although we consider Alexandrov spaces with curvature bounded below, the results are new even in the Riemannian case.
Keywords:
alexandrov spaces;
obtuse constants;
constants alexandrov
Journal Title: Journal of the Mathematical Society of Japan
Year Published: 2019
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Journal Title: Journal of the Mathematical Society of Japan
Year Published: 2019
Link to full text (if available)
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recommendations!