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arXiv · 1304.7464

An analytical approach to the Rational Simplex Problem

Victor Alexandrov
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Abstract

In 1973, J. Cheeger and J. Simons raised the following question that still remains open and is known as the Rational Simplex Problem: Given a geodesic simplex in the spherical 3-space so that all of its interior dihedral angles are rational multiples of $\pi$, is it true that its volume is a rational multiple of the volume of the 3-sphere? We propose an analytical approach to the Rational Simplex Problem by deriving a function $f(t)$, defined as an integral of an elementary function, such that if there is a rational $t$, close enough to zero, such that the value $f(t)$ is an irrational number then the answer to the Rational Simplex Problem is negative.

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Victor Alexandrov. 2013-04-28. An analytical approach to the Rational Simplex Problem. https://arxiv.org/abs/1304.7464

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