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The Lipschitz constant of convex sphere in R^3$\mathbb{R}^3$

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mmaatthh
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Convex The Lipschitz constant of convex sphere in R^3

Is every convex sphere (in the sense of Alexandorff, which is the boundary of some convex body in $\mathbb{R}^3$) with Alexandorff curvature $\geq 1$, bi-Lipschitzadmitting a bijective map to the unit round sphere in $\mathbb{R}^3$ with Lipschitz constant $\leq 1$?

Convex sphere in R^3

Is every convex sphere (in the sense of Alexandorff, which is the boundary of some convex body in $\mathbb{R}^3$) with Alexandorff curvature $\geq 1$, bi-Lipschitz to the unit round sphere in $\mathbb{R}^3$?

The Lipschitz constant of convex sphere in R^3

Is every convex sphere (in the sense of Alexandorff, which is the boundary of some convex body in $\mathbb{R}^3$) with Alexandorff curvature $\geq 1$, admitting a bijective map to the unit round sphere in $\mathbb{R}^3$ with Lipschitz constant $\leq 1$?

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mmaatthh
  • 799
  • 5
  • 10

Convex sphere in R^3

Is every convex sphere (in the sense of Alexandorff, which is the boundary of some convex body in $\mathbb{R}^3$) with Alexandorff curvature $\geq 1$, bi-Lipschitz to the unit round sphere in $\mathbb{R}^3$?