On Schläfli's reduction formula.

Ruth Kellerhals

Displaying similar documents to “On Schläfli's reduction formula.”

Volumes in Hyperbolic 5-space.

R. Kellerhals (1995)

Geometric and functional analysis

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A priori estimates for higher order hyperbolic equations.

Mitsuru Sugimoto (1994)

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Chiral Polytopes from Hyperbolic Honeycombs.

E. Schulte, B. Nostrand (1995)

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An illustrated theory of hyperbolic virtual polytopes

Marina Knyazeva, Gaiane Panina (2008)

Open Mathematics

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The paper gives an illustrated introduction to the theory of hyperbolic virtual polytopes and related counterexamples to A.D. Alexandrov’s conjecture.

On hyperbolic virtual polytopes and hyperbolic fans

Gaiane Panina (2006)

Open Mathematics

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Hyperbolic virtual polytopes arose originally as polytopal versions of counterexamples to the following A.D.Alexandrov’s uniqueness conjecture: Let K ⊂ ℝ3 be a smooth convex body. If for a constant C, at every point of ∂K, we have R 1 ≤ C ≤ R 2 then K is a ball. (R 1 and R 2 stand for the principal curvature radii of ∂K.) This paper gives a new (in comparison with the previous construction by Y.Martinez-Maure and by G.Panina) series of counterexamples to the conjecture. In particular,...