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Mat. Sb., 2008, Volume 199, Number 10, Pages 41–62 (Mi msb3956)  

This article is cited in 9 scientific papers (total in 9 papers)

Dual theorems on central points and their generalizations

R. N. Karasev

Moscow Institute of Physics and Technology

Abstract: Analogues of theorems on a central point, a central transversal and also of Tverberg's theorem are proved in the context when arrangements of hyperplanes or planes of fixed dimension are considered in place of point sets.
Bibliography: 20 titles.

Keywords: center point theorem, Tverberg's theorem, Brower's fixed point theorem

DOI: https://doi.org/10.4213/sm3956

Full text: PDF file (552 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2008, 199:10, 1459–1479

Bibliographic databases:

UDC: 514.174
MSC: Primary 52A37; Secondary 55R10
Received: 15.10.2007 and 04.03.2008

Citation: R. N. Karasev, “Dual theorems on central points and their generalizations”, Mat. Sb., 199:10 (2008), 41–62; Sb. Math., 199:10 (2008), 1459–1479

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  • https://doi.org/10.4213/sm3956
  • http://mi.mathnet.ru/eng/msb/v199/i10/p41

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. R. N. Karasev, “Topological methods in combinatorial geometry”, Russian Math. Surveys, 63:6 (2008), 1031–1078  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. Karasev R.N., “Equipartition of a measure by $(Z_p)^k$-invariant fans”, Discrete Comput. Geom., 43:2 (2010), 477–481  crossref  mathscinet  zmath  isi  elib  scopus
    3. Karasev R.N., “Tverberg-type theorems for intersecting by rays”, Discrete Comput. Geom., 45:2 (2011), 340–347  crossref  mathscinet  zmath  isi  elib  scopus
    4. Karasev R.N., “Analogues of the central point theorem for families with d-intersection property in $\mathbb R^d$”, Combinatorica, 32:6 (2012), 689–702  crossref  mathscinet  zmath  isi  elib  scopus
    5. Bárány I. Karasev R., “Notes about the Carathéodory number”, Discret. Comput. Geom., 48:3 (2012), 783–792  crossref  mathscinet  zmath  isi  elib  scopus
    6. Barany I., Pach J., “Homogeneous Selections From Hyperplanes”, J. Comb. Theory Ser. B, 104 (2014), 81–87  crossref  mathscinet  zmath  isi  scopus
    7. Roman Karasev, Benjamin Matschke, “Projective Center Point and Tverberg Theorems”, Discrete Comput Geom, 2014  crossref  mathscinet  scopus
    8. Barany I., Soberon P., “Tverberg'S Theorem Is 50 Years Old: a Survey”, Bull. Amer. Math. Soc., 55:4 (2018), 459–492  crossref  mathscinet  zmath  isi  scopus
    9. Lee S., Yoo K., “On a Conjecture of Karasev”, Comput. Geom.-Theory Appl., 75 (2018), 1–10  crossref  mathscinet  zmath  isi  scopus
  • Математический сборник Sbornik: Mathematics (from 1967)
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