An integer parallelotope with small surface area

Assaf Naor; Oded Regev

doi:10.1016/j.jfa.2023.110122

An integer parallelotope with small surface area

Assaf Naor, Oded Regev

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We prove that for any n∈N there is a convex body K⊆Rⁿ whose surface area is at most n^{[Formula presented]+o(1)}, yet the translates of K by the integer lattice Zⁿ tile Rⁿ.

Original language	English (US)
Article number	110122
Journal	Journal of Functional Analysis
Volume	285
Issue number	10
DOIs	https://doi.org/10.1016/j.jfa.2023.110122
State	Published - Nov 15 2023

All Science Journal Classification (ASJC) codes

Analysis

Keywords

Integer lattice
Surface area
Tiling bodies

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10.1016/j.jfa.2023.110122

Cite this

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title = "An integer parallelotope with small surface area",

abstract = "We prove that for any n∈N there is a convex body K⊆Rn whose surface area is at most n[Formula presented]+o(1), yet the translates of K by the integer lattice Zn tile Rn.",

keywords = "Integer lattice, Surface area, Tiling bodies",

author = "Assaf Naor and Oded Regev",

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year = "2023",

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doi = "10.1016/j.jfa.2023.110122",

language = "English (US)",

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AU - Naor, Assaf

AU - Regev, Oded

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N2 - We prove that for any n∈N there is a convex body K⊆Rn whose surface area is at most n[Formula presented]+o(1), yet the translates of K by the integer lattice Zn tile Rn.

AB - We prove that for any n∈N there is a convex body K⊆Rn whose surface area is at most n[Formula presented]+o(1), yet the translates of K by the integer lattice Zn tile Rn.

KW - Integer lattice

KW - Surface area

KW - Tiling bodies

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JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

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An integer parallelotope with small surface area

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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