243 research outputs found
On the Alexandrov problem of distance preserving mapping
No full textAbstractIn this paper the author has studied the Alexandrov problem of area preserving mappings in linear 2-normed spaces and has provided some remarks for the generalization of earlier results of H.Y. Chu, C.G. Park and W.G. Park.In addition the author has introduced the concept of linear (2,p)-normed spaces and for such spaces he has solved the Alexandrov problem
First variation formula in Wasserstein spaces over compact Alexandrov spaces
No full textWe extend results proved by the second author (Amer. J. Math., 2009) for nonnegatively curved Alexandrov spaces to general compact Alexandrov spaces X with curvature bounded below. The gradient flow of a geodesically convex functional on the quadratic Wasserstein space (P(X),W_2) satisfies the evolution variational inequality. Moreover, the gradient flow enjoys uniqueness and contractivity. These results are obtained by proving a first variation formula for the Wasserstein distance. © Canadian Mathematical Society 2011
Analytic approaches and harmonic functions on Alexandrov spaces with nonnegative Ricci curvature
No full textAbstractIn this paper, the author gets a sharp dimension estimate of the space of harmonic functions with polynomial growth of a fixed order on Alexandrov spaces, which extends the result of Colding and Minicozzi from Riemannian manifolds to Alexandrov spaces
Compactness of Alexandrov-Nirenberg Surfaces
No full textWe study a class of compact surfaces in R-3 introduced by Alexandrov and generalized by Nirenberg and prove a compactness result under suitable assumptions on induced metrics and Gauss curvatures. (c) 2017 Wiley Periodicals, Inc.National Science Foundation [DMS-140459]; National Natural Science Foundation of China [11121101, 11131005]SCI(E)ARTICLE91706-17537
Intersection numbers on M¯ g,n and BKP hierarchy
No full text© 2021, The Author(s).In their recent inspiring paper, Mironov and Morozov claim a surprisingly simple expansion formula for the Kontsevich-Witten tau-function in terms of the Schur Q-functions. Here we provide a similar description for the Brézin-Gross-Witten tau-function. Moreover, we identify both tau-functions of the KdV hierarchy, which describe intersection numbers on the moduli spaces of punctured Riemann surfaces, with the hypergeometric solutions of the BKP hierarchy.11Nsciescopu
To the memory of Boris Alexandrov and Galina Ivanovich
No full textOn December 4, 2019, teams of Institute of Marine Biology of the National Academy of Sciences of Ukraine (Odessa) and A. O. Kovalevsky Institute of Biology of the Southern Seas of Russian Academy of Sciences (Sevastopol) suffered a painful and irreparable double loss: Director of IMB D. Sc., Prof. Boris Alexandrov and senior scientist, PhD Galina Ivanovich tragically perished in a terrible fire in the building of Odessa IMB. Boris Alexandrov was a talented scientist in marine ecology, widely-known expert in international hydrobiological community, as well as an outstanding teacher and respectful leader of a large Institute’s staff. Boris Alexandrov lived a remarkable and active life of only 61 years. List of his scientific merits and achievements is impressive: Doctor of Biological Sciences, Professor, Corresponding Member of NAS of Ukraine, laureate of the State Prize for Science and Technology of Ukraine, Honoured Worker of Science and Techniques of Ukraine, author of the more than 200 scientific papers and monographs. For more than 10 years, Boris Alexandrov was the Head of the Biodiversity Conservation Expert Group in the Black Sea Commission for protection of the marine ecosystems against pollution. Galina Ivanovich was expert in physiology of marine organisms. Since the beginning of her research career (1985), she worked at Odessa IMB, and published more than 50 scientific articles. The blessed memory of Boris Alexandrov and Galina Ivanovich will forever remain in our hearts
Refined open intersection numbers and the Kontsevich-Penner matrix model
No full textA study of the intersection theory on the moduli space of Riemann surfaces with boundary was recently initiated in a work of R. Pandharipande, J.P. Solomon and the third author, where they introduced open intersection numbers in genus 0. Their construction was later generalized to all genera by J.P. Solomon and the third author. In this paper we consider a refinement of the open intersection numbers by distinguishing contributions from surfaces with different numbers of boundary components, and we calculate all these numbers. We then construct a matrix model for the generating series of the refined open intersection numbers and conjecture that it is equivalent to the Kontsevich-Penner matrix model. An evidence for the conjecture is presented. Another refinement of the open intersection numbers, which describes the distribution of the boundary marked points on the boundary components, is also discussed
Quasigeodesics in multidimensional Alexandrov spaces
No full textHere we generalize quasigeodesics to multidimensional Alexandrov space with curvature bounded from below and prove that classical theorems of Alexandrov also hold for this case. Also we develop gradient curves as a tool for studying spaces with curvature bounded from below.In the second chapter we give some applications of quasigeodesics and gradient curves: the Radius Sphere theorem, the Glueing theorem and the First variation formula for extremal subsets.Made available in DSpace on 2011-05-07T14:04:30Z (GMT). No. of bitstreams: 2
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An Alexandrov theorem in Minkowski spacetime
No full textInternational audienceIn this paper, we generalize a theorem à la Alexandrov of Wang, Wang and Zhang [WWZ] for closed codimension-two spacelike submanifolds in the Minkowski spacetime for an adapted CMC condition
A Form of Alexandrov-Fenchel Inequality
No full textWe give a proof of the Alexandrov-Fenchel type inequality for k-convex function on S(n).http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000274659000002&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=8e1609b174ce4e31116a60747a720701Mathematics, AppliedMathematicsSCI(E)6ARTICLE4999-1012
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