Zobrazeno 1 - 10
of 2 091
pro vyhledávání: '"A. Petrunin"'
Autor:
Petrunin, Anton
Suppose M is a closed submanifold in a Euclidean ball of large dimension. We give an optimal bound on the normal curvatures that guarantee that M is a sphere. The border cases consist of Veronese embeddings of the four projective planes.
Comment
Comment
Externí odkaz:
http://arxiv.org/abs/2408.05909
Autor:
Petrunin, Anton
We consider the following question: When does a Riemannian manifold admit an embedding with a uniformly thick tubular neighborhood in another Riemannian manifold of large dimension?
Comment: 12 pages 3 figures
Comment: 12 pages 3 figures
Externí odkaz:
http://arxiv.org/abs/2402.16195
Autor:
Petrunin, Anton
Publikováno v:
Geom. Funct. Anal. 34 (2024), no.1, 202--208
We give an optimal bound on normal curvatures of immersed n-torus in a Euclidean ball of large dimension.
Comment: 6 pages, 1 figure
Comment: 6 pages, 1 figure
Externí odkaz:
http://arxiv.org/abs/2304.00886
Autor:
Lebedeva, Nina, Petrunin, Anton
Written for the book "Mathematicians from Saint Petersburg and their theorems".
Comment: english+russian
Comment: english+russian
Externí odkaz:
http://arxiv.org/abs/2212.10479
Autor:
Lebedeva, Nina, Petrunin, Anton
Publikováno v:
Sib. Math. J. 64, 624--628 (2023)
Graph comparison is a certain type of condition on metric space encoded by a finite graph. We show that any nontrivial graph comparison implies one of Alexandrov's comparisons. The proof gives a complete description of graphs with trivial graph compa
Externí odkaz:
http://arxiv.org/abs/2212.08016
Autor:
Lebedeva, Nina, Petrunin, Anton
We show that trees and their products meet octahedron comparison.
Comment: 4 pages, 4 figures
Comment: 4 pages, 4 figures
Externí odkaz:
http://arxiv.org/abs/2212.06445
Publikováno v:
Известия высших учебных заведений. Поволжский регион: Медицинские науки, Iss 2 (2024)
Background. Echinococcosis is an endemic disease that is accompanied by severe complications and a high recurrence rate. The lack of unified approaches to the choice of surgical treatment and principles of prevention arouses interest in this disease
Externí odkaz:
https://doaj.org/article/bb67a1bacbf7421e8c256849babe1cdb
Autor:
Lebedeva, Nina, Petrunin, Anton
Publikováno v:
Algebra i Analiz 35:3 (2023), 52--56
A metric space is said to be all-set-homogeneous if any of its partial isometries can be extended to a genuine isometry. We give a classification of a certain subclass of all-set-homogeneous length spaces.
Comment: English+Russian, 4+4 pages, 1+
Comment: English+Russian, 4+4 pages, 1+
Externí odkaz:
http://arxiv.org/abs/2211.09671
Micro- and nanogels are widely used to stabilise emulsions and simultaneously implement their responsiveness to the external stimuli. One of the factors that improves the emulsion stability is the nanogel softness. Here, we study how the softest nano
Externí odkaz:
http://arxiv.org/abs/2208.08185
Autor:
Petrunin, Anton
Publikováno v:
Turkish J. Math. 27 (2003), no. 1, 173--187
We give a condition on the curvature tensors of Riemannian manifolds that admit Lipschitz approximation by polyhedral metrics with curvature bounded below or above. We show that this condition is also sufficient for the existence of local approximati
Externí odkaz:
http://arxiv.org/abs/2207.07559