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The hyperbolic space $\mathbb H3$, has a boundary $\mathbb CP1$.

A ideal tetrahedron in $\mathbb H3$, is a tetrahedron, where the four vertices are on the boundary $\mathbb CP1$.

The four vertices of the tetrahedron may be parametrized by four complex $z1, z2, z3, z4$

What is the surface of this ideal tetrahedron, as function of $z1, z2, z3, z4$ ?.

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1 Answer 1

Answer from Igor Rivin (http://mathoverflow.net/users/11142/igor-rivin) :

The answer is $4 \pi$

The surface of a tetrahedron is the union of four ideal triangles, all of which have area π.

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