Subdividing a Convex Body by a System of Cones and Polytopes Inscribed in the Body

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Subdividing a Convex Body by a System of Cones and Polytopes Inscribed in the Body. / Makeev, V. V.; Netsvetaev, N. Yu.

In: Journal of Mathematical Sciences, Vol. 251, No. 4, 12.2020, p. 512-515.

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

BibTeX

@article{1e569f82cabd46a68f76bf10147d8f69,

title = "Subdividing a Convex Body by a System of Cones and Polytopes Inscribed in the Body",

abstract = "The literature contains quite a few theorems on subdividing the volume of a convex body by a system of cones and on the possibility to circumscribe the body about a polytope of one type or another. See R. N. Karasev, “Topological methods in combinatorial geometry,” Russian Math. Surveys, 63, No. 6, 1031–1078 (2008) for a survey of similar results. In the following, we also prove theorems of this kind. As a limit case, we obtain well-known theorems on inscribed polytopes.",

author = "Makeev, {V. V.} and Netsvetaev, {N. Yu}",

year = "2020",

month = dec,

doi = "10.1007/s10958-020-05110-7",

language = "English",

volume = "251",

pages = "512--515",

journal = "Journal of Mathematical Sciences",

issn = "1072-3374",

publisher = "Springer Nature",

number = "4",

}

RIS

TY - JOUR

T1 - Subdividing a Convex Body by a System of Cones and Polytopes Inscribed in the Body

AU - Makeev, V. V.

AU - Netsvetaev, N. Yu

PY - 2020/12

Y1 - 2020/12

N2 - The literature contains quite a few theorems on subdividing the volume of a convex body by a system of cones and on the possibility to circumscribe the body about a polytope of one type or another. See R. N. Karasev, “Topological methods in combinatorial geometry,” Russian Math. Surveys, 63, No. 6, 1031–1078 (2008) for a survey of similar results. In the following, we also prove theorems of this kind. As a limit case, we obtain well-known theorems on inscribed polytopes.

AB - The literature contains quite a few theorems on subdividing the volume of a convex body by a system of cones and on the possibility to circumscribe the body about a polytope of one type or another. See R. N. Karasev, “Topological methods in combinatorial geometry,” Russian Math. Surveys, 63, No. 6, 1031–1078 (2008) for a survey of similar results. In the following, we also prove theorems of this kind. As a limit case, we obtain well-known theorems on inscribed polytopes.

UR - http://www.scopus.com/inward/record.url?scp=85095692723&partnerID=8YFLogxK

U2 - 10.1007/s10958-020-05110-7

DO - 10.1007/s10958-020-05110-7

M3 - Article

AN - SCOPUS:85095692723

VL - 251

SP - 512

EP - 515

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 4

ER -

ID: 75575160