Improved bounds for Hadwiger’s covering problem via thin-shell estimates

  title={Improved bounds for Hadwiger’s covering problem via thin-shell estimates},
  author={Han Huang and Boaz A. Slomka and Tomasz Tkocz and Beatrice-Helen Vritsiou},
  journal={Journal of the European Mathematical Society},
A central problem in discrete geometry, known as Hadwiger's covering problem, asks what the smallest natural number $N\left(n\right)$ is such that every convex body in ${\mathbb R}^{n}$ can be covered by a union of the interiors of at most $N\left(n\right)$ of its translates. Despite continuous efforts, the best general upper bound known for this number remains as it was more than sixty years ago, of the order of ${2n \choose n}n\ln n$. In this note, we improve this bound by a sub-exponential… 

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