36 citations · 170 across the 43 of their papers we have counts for
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Computation of homogenized stiffnesses of thin corrugated plates
A. A. Kolpakov, A. G. Kolpakov
The homogenized stiffnesses of a corrugated plate are calculated by solving the periodicity cell problem of the homogenization theory by using two-steps dimension reduction procedu…
Spherical tetrahedra with rational volume, and spherical Pythagorean triples
Alexander Kolpakov, Sinai Robins
We study spherical tetrahedra with rational dihedral angles and rational volumes. Such tetrahedra occur in the Rational Simplex Conjecture by Cheeger and Simons, and we supply vast…
Many cusped hyperbolic 3-manifolds do not bound geometrically
Alexander Kolpakov, Alan W. Reid, Stefano Riolo
In this note, we show that there exist cusped hyperbolic -manifolds that embed geodesically, but cannot bound geometrically. Thus, being a geometric boundary is a non-trivial pr…
Spherical and geodesic growth rates of right-angled Coxeter and Artin groups are Perron numbers
Alexander Kolpakov, Alexey Talambutsa
We prove that for any infinite right-angled Coxeter or Artin group, its spherical and geodesic growth rates (with respect to the standard generating set) either take values in the…