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Matematicheskie Zametki, 2012, Volume 91, Issue 3, Pages 440–458
DOI: https://doi.org/10.4213/mzm8567 (Mi mzm8567) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Completions of Convex Families of Convex Bodies

A. G. Khovanskii

Institute of Systems Analysis, Russian Academy of Sciences
Full-text PDF (535 kB) Citations (4)
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DOI: https://doi.org/10.4213/mzm8567
Abstract: The paper discusses the existence of a continuous extension of functions that are defined on subsets of $\mathbb R^n$ and whose values are convex bodies in $\mathbb R^n$. This problem arose in convex geometry in connection with the notion, recently introduced in algebraic geometry, of convex Newton–Okounkov bodies.
Keywords: Newton–Okounkov body, convex-valued function, continuity, extension.
Received: 10.06.2009
Revised: 13.07.2011
English version:
Mathematical Notes, 2012, Volume 91, Issue 3, Pages 415–429
DOI: https://doi.org/10.1134/S000143461203011X
Bibliographic databases:
Document Type: Article
UDC: 514.172.4
Language: Russian
Citation: A. G. Khovanskii, “Completions of Convex Families of Convex Bodies”, Mat. Zametki, 91:3 (2012), 440–458; Math. Notes, 91:3 (2012), 415–429
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/mzm8567
  • https://doi.org/10.4213/mzm8567
  • https://www.mathnet.ru/eng/mzm/v91/i3/p440
    • This publication is cited in the following 4 articles:
    1. Debam Biswas, “Convex bodies associated to linear series of adelic divisors on quasi-projective varieties”, Beitr Algebra Geom, 2024  crossref
    2. Irina V. Polikanova, “On the Boundaries of Sets and Boundaries of Convex Sets”, Izvestiya AltGU, 2024, no. 1(135), 120  crossref
    3. Léo Mathis, Chiara Meroni, “Fiber Convex Bodies”, Discrete Comput Geom, 70:4 (2023), 1451  crossref
    4. Kaveh K., Khovanskii A.G., “Newton-Okounkov bodies, semigroups of integral points, graded algebras and intersection theory”, Ann. of Math. (2), 176:2 (2012), 925–978  crossref  mathscinet  zmath  isi  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические заметки Mathematical Notes
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    Abstract page:475
    Full-text PDF :185
    References:49
    First page:36
     
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