3 papers
math.MG2026
Illumination number of 3-dimensional cap bodies
Andrii Arman, Jaskaran Singh Kaire, Andriy Prymak
The illumination conjecture asserts that any convex body in -dimensional Euclidean space can be illuminated by at most external light sources or parallel beams of light. D…
math.MG2025
Hadwiger's conjecture for cap bodies
Andrii Arman, Jaskaran Singh Kaire, Andriy Prymak
Hadwiger's covering conjecture states that every -dimensional convex body can be covered by at most of its smaller positive homothetic translates, with copies requir…
math.CA2025
Whitney-type estimates for convex functions
Jaskaran Singh Kaire, Andriy Prymak
We study Whitney-type estimates for approximation of convex functions in the uniform norm on various convex multivariate domains while paying a particular attention to the dependen…