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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.MG2025
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…