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

1 Scopus citations

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

Access to Document

10.1016/j.jfa.2023.110122

Cite this

@article{d77fd9583c664ae0b16fbe3cabc94d06,

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",

note = "Publisher Copyright: {\textcopyright} 2023 Elsevier Inc.",

year = "2023",

month = nov,

day = "15",

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

language = "English (US)",

volume = "285",

journal = "Journal of Functional Analysis",

issn = "0022-1236",

publisher = "Academic Press Inc.",

number = "10",

}

TY - JOUR

T1 - An integer parallelotope with small surface area

AU - Naor, Assaf

AU - Regev, Oded

PY - 2023/11/15

Y1 - 2023/11/15

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

UR - https://www.scopus.com/pages/publications/85168001527

UR - https://www.scopus.com/inward/citedby.url?scp=85168001527&partnerID=8YFLogxK

U2 - 10.1016/j.jfa.2023.110122

DO - 10.1016/j.jfa.2023.110122

M3 - Article

AN - SCOPUS:85168001527

SN - 0022-1236

VL - 285

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 10

M1 - 110122

ER -

An integer parallelotope with small surface area

Abstract

All Science Journal Classification (ASJC) codes

Keywords

Access to Document

Other files and links

Fingerprint

Cite this