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math.MG2025
Metric complexity is a Bryant--Tupper diversity
Gautam Aishwarya, Dongbin Li, Mokshay Madiman +1
The metric complexity (sometimes called Leinster--Cobbold maximum diversity) of a compact metric space is a recently introduced isometry-invariant of compact metric spaces which ge…
math.MG2024
The Kneser--Poulsen phenomena for entropy
Gautam Aishwarya, Dongbin Li
The Kneser--Poulsen conjecture asserts that the volume of a union of balls in Euclidean space cannot be increased by bringing their centres pairwise closer. We prove that its natur…
math.MG2022★ 2 cited
Entropic exercises around the Kneser-Poulsen conjecture
Gautam Aishwarya, Irfan Alam, Dongbin Li +2
We develop an information-theoretic approach to study the Kneser--Poulsen conjecture in discrete geometry. This leads us to a broad question regarding whether Rényi entropies of in…