<div class="csl-bib-body">
<div class="csl-entry">Brauner, L., & Ortega Moreno, O. A. (2023). <i>Fixed Points of Mean Section Operators</i>. arXiv. https://doi.org/10.48550/arXiv.2302.11973</div>
</div>
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/190827
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dc.description.abstract
We characterize rotation equivariant bounded linear operators from $C(\S^{n-1})$ to $C^2(\S^{n-1})$ by the mass distribution of the spherical Laplacian of their kernel function on small polar caps. Using this characterization, we show that every continuous, homogeneous, translation invariant, and rotation equivariant Minkowski valuation $\Phi$ that is weakly monotone maps the space of convex bodies with a $C^2$ support function into itself. As an application, we prove that if $\Phi$ is in addition even or a mean section operator, then Euclidean balls are its only fixed points in some $C^2$ neighborhood of the unit ball. Our approach unifies and extends previous results by Ivaki from 2017 and the second author together with Schuster from 2021.
en
dc.description.sponsorship
FWF - Österr. Wissenschaftsfonds
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dc.description.sponsorship
FWF - Österr. Wissenschaftsfonds
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dc.language.iso
en
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dc.subject
Minkowski valuation
en
dc.subject
convex geometry
en
dc.subject
Mean section operators
en
dc.subject
fixed points
en
dc.title
Fixed Points of Mean Section Operators
en
dc.type
Preprint
en
dc.type
Preprint
de
dc.identifier.arxiv
2302.11973
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dc.relation.grantno
ESP 236-N
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dc.relation.grantno
P31448-N35
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tuw.project.title
Fixpunkt Probleme und isoperimetrische Ungleichungen
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tuw.project.title
Affine isoperimetrische Ungleichungen
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tuw.researchTopic.id
A3
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tuw.researchTopic.name
Fundamental Mathematics Research
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tuw.researchTopic.value
100
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tuw.publication.orgunit
E104-07 - Forschungsbereich Geometrische Analysis
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tuw.publisher.doi
10.48550/arXiv.2302.11973
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tuw.publisher.server
arXiv
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wb.sciencebranch
Mathematik
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wb.sciencebranch.oefos
1010
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wb.sciencebranch.value
100
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item.languageiso639-1
en
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item.openairetype
preprint
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item.cerifentitytype
Publications
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item.grantfulltext
none
-
item.fulltext
no Fulltext
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item.openairecristype
http://purl.org/coar/resource_type/c_816b
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crisitem.author.dept
E104-07 - Forschungsbereich Geometrische Analysis
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crisitem.author.dept
E104-07 - Forschungsbereich Geometrische Analysis
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crisitem.author.parentorg
E104 - Institut für Diskrete Mathematik und Geometrie
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crisitem.author.parentorg
E104 - Institut für Diskrete Mathematik und Geometrie