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3 results for “Atkinson”

Volume estimates for right-angled hyperbolic polyhedramath.GT

Improved volume estimates for right-angled polyhedra in hyperbolic space.

problem Estimating volumes of right-angled polyhedra in hyperbolic space.

method Combining Andreev theorem and Atkinson's results, improved upper volume estimates.

result Upper volume estimates for both compact and ideal right-angled polyhedra improved.

hyperbolic geometry polyhedra volume estimates Andreev theorem Atkinson

2020-10-21abs ↗pdf ↗

A sequence of

π/3

-equiangular hyperbolic polyhedramath.GT

New hyperbolic polyhedra with $π/3$ angles and volumes calculated.

problem Finding new hyperbolic polyhedra with specific dihedral angles.

method Constructed a new sequence of hyperbolic polyhedra with

π/3

angles and determined their volumes.

result Volumes of some constructed polyhedra determined.

hyperbolic polyhedra π/3 angles volumes

2024-01-23abs ↗pdf ↗

Sturm-Liouville Estimates for the Spectrum and Cheeger Constantmath.DG

Buser's inequality gives an upper bound on the first non-zero eigenvalue of the Laplacian of a closed manifold M in terms of the Cheeger constant h(M). Agol later gave a quantitative improvement of Buser's inequality. Agol's result is less transparent since it is given implicitly by a set of equations, one of which is …

2013-08-27abs ↗pdf ↗