Zobrazeno 1 - 10
of 45
pro vyhledávání: '"Anton Petrunin"'
Autor:
Alexander Lytchak, Anton Petrunin
Publikováno v:
Journal of Optimization Theory and Applications. 194:636-642
We show that cyclic products of projections onto convex subsets of Hadamard spaces can behave in a more complicated way than in Hilbert spaces, resolving a problem formulated by Miroslav Ba\v{c}\'ak. Namely, we construct an example of convex subsets
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6404aa5837e6261848a68231d54a160d
https://doi.org/10.1007/s10957-022-02043-w
https://doi.org/10.1007/s10957-022-02043-w
Publikováno v:
The American Mathematical Monthly. 129:475-479
We present a proof of the Moon in a puddle theorem, and use its key lemma to prove a generalization of the four-vertex theorem.
Comment: 5 pges, 6 figure. arXiv admin note: text overlap with arXiv:2012.11814
Comment: 5 pges, 6 figure. arXiv admin note: text overlap with arXiv:2012.11814
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9e871f87ecbf505bbff38e2d9adb774d
https://doi.org/10.1080/00029890.2022.2041355
https://doi.org/10.1080/00029890.2022.2041355
Autor:
Nina Lebedeva, Anton Petrunin
Publikováno v:
Analysis and Geometry in Metric Spaces, Vol 9, Iss 1, Pp 160-166 (2021)
We give another proof of Toyoda's theorem that describes 5-point subpaces in CAT(0) length spaces
Comment: 9 pages, 8 figures
Comment: 9 pages, 8 figures
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f232c9680f9291b799fe03714f484181
https://doaj.org/article/dff9eb07e2b644dc85c316513803bd07
https://doaj.org/article/dff9eb07e2b644dc85c316513803bd07
Autor:
Anton Petrunin
Publikováno v:
The Mathematical Intelligencer. 43:16-18
We discuss self-crossing patterns of closed geodesics on a convex surface.
3 pages, 10 figures
3 pages, 10 figures
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::dd514f8b835a8c1510deaa5190fa0b6c
https://doi.org/10.1007/s00283-021-10127-0
https://doi.org/10.1007/s00283-021-10127-0
Autor:
Alexander Lytchak, Anton Petrunin
Publikováno v:
Proceedings of the American Mathematical Society. 149:1247-1257
We construct short retractions of a CAT(1) space to its small convex subsets. This construction provides an alternative geometric description of an analytic tool introduced by Wilfrid Kendall. Our construction uses a tractrix flow which can be define
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::395430755372baa87dcef8577a5b513e
https://doi.org/10.1090/proc/15268
https://doi.org/10.1090/proc/15268
Autor:
Nina Lebedeva, Anton Petrunin
We give an if-and-only-if condition on a five-point metric spaces that admit embeddings into nonnegatively curved Riemannian manifolds.
Comment: 19 pages, 37 figures
Comment: 19 pages, 37 figures
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::3df77a08dde6136984773c2aa02370f8
Autor:
Nina Lebedeva, Anton Petrunin
We show that trees and their products meet octahedron comparison.
Comment: 4 pages, 4 figures
Comment: 4 pages, 4 figures
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a1bcab2f235397a331375ae1003b710b
Autor:
Anton Petrunin, Stephan Stadler
Publikováno v:
Geom. Topol. 23, no. 6 (2019), 3111-3139
A surface which does not admit a length nonincreasing deformation is called metric minimizing. We show that metric minimizing surfaces in CAT(0) spaces are locally CAT(0) with respect to their intrinsic metric.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6c1359f73b3256eec4dfae42361048c6
https://doi.org/10.2140/gt.2019.23.3111
https://doi.org/10.2140/gt.2019.23.3111
Alexandrov spaces are defined via axioms similar to those of the Euclid axioms but where certain equalities are replaced with inequalities. Depending on the signs of the inequalities, we obtain Alexandrov spaces with curvature bounded above (CBA) and
Autor:
Anton Petrunin
This book serves as an introductory asset for learning metric geometry by delivering an in-depth examination of key constructions and providing an analysis of universal spaces, injective spaces, the Gromov-Hausdorff convergence, and ultralimits. This