We show that the model surface of a germ of a holomorphically homogeneous CR-manifold is holomorphically homogeneous. We also obtain restrictions on the multiplicities in the Bloom–Graham type of a germ of a holomorphically homogeneous CR-manifold.
{"title":"Holomorphically homogeneous CR-manifolds and their model surfaces","authors":"M. Stepanova","doi":"10.1070/IM9056","DOIUrl":"https://doi.org/10.1070/IM9056","url":null,"abstract":"We show that the model surface of a germ of a holomorphically homogeneous CR-manifold is holomorphically homogeneous. We also obtain restrictions on the multiplicities in the Bloom–Graham type of a germ of a holomorphically homogeneous CR-manifold.","PeriodicalId":54910,"journal":{"name":"Izvestiya Mathematics","volume":"85 1","pages":"529 - 535"},"PeriodicalIF":0.8,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43333712","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper we prove the birational superrigidity of Fano–Mori fibre spaces all of whose fibres are complete intersections of type in the projective space satisfying certain conditions of general position, under the assumption that the fibration is sufficiently twisted over the base (in particular, under the assumption that the -condition holds). The condition of general position for every fibre guarantees that the global log canonical threshold is equal to one. This condition also bounds the dimension of the base by a constant depending only on the dimension of the fibre (this constant grows like as ). The fibres and the variety may have quadratic and bi-quadratic singularities whose rank is bounded below.
{"title":"Birational geometry of varieties fibred into complete intersections of codimension two","authors":"A. Pukhlikov","doi":"10.1070/IM9146","DOIUrl":"https://doi.org/10.1070/IM9146","url":null,"abstract":"In this paper we prove the birational superrigidity of Fano–Mori fibre spaces all of whose fibres are complete intersections of type in the projective space satisfying certain conditions of general position, under the assumption that the fibration is sufficiently twisted over the base (in particular, under the assumption that the -condition holds). The condition of general position for every fibre guarantees that the global log canonical threshold is equal to one. This condition also bounds the dimension of the base by a constant depending only on the dimension of the fibre (this constant grows like as ). The fibres and the variety may have quadratic and bi-quadratic singularities whose rank is bounded below.","PeriodicalId":54910,"journal":{"name":"Izvestiya Mathematics","volume":"86 1","pages":"334 - 411"},"PeriodicalIF":0.8,"publicationDate":"2021-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44736620","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We obtain capacitive criteria for the approximability of individual functions by solutions of second-order homogeneous elliptic equations with constant complex coefficients in the norm of a Whitney-type -space on a compact set in , . The case was studied in a recent paper by the author and Tolsa. For -approximations by harmonic functions (with any ), weaker criteria were earlier found by the author. We establish some metric properties of the capacities considered.
{"title":"Criteria for -approximability of functions on compact sets in , , by solutions of second-order homogeneous elliptic equations","authors":"P. V. Paramonov","doi":"10.1070/IM9036","DOIUrl":"https://doi.org/10.1070/IM9036","url":null,"abstract":"We obtain capacitive criteria for the approximability of individual functions by solutions of second-order homogeneous elliptic equations with constant complex coefficients in the norm of a Whitney-type -space on a compact set in , . The case was studied in a recent paper by the author and Tolsa. For -approximations by harmonic functions (with any ), weaker criteria were earlier found by the author. We establish some metric properties of the capacities considered.","PeriodicalId":54910,"journal":{"name":"Izvestiya Mathematics","volume":"85 1","pages":"483 - 505"},"PeriodicalIF":0.8,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58574816","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We obtain a lower bound for the rate of convergence of multipoint Padé approximants of functions holomorphically extendable from a compact set to a union of domains whose boundaries possess a symmetry property. The bound obtained matches a known upper bound for the same quantity.
{"title":"On a lower bound for the rate of convergence of multipoint Padé approximants of piecewise analytic functions","authors":"V. Buslaev","doi":"10.1070/IM9047","DOIUrl":"https://doi.org/10.1070/IM9047","url":null,"abstract":"We obtain a lower bound for the rate of convergence of multipoint Padé approximants of functions holomorphically extendable from a compact set to a union of domains whose boundaries possess a symmetry property. The bound obtained matches a known upper bound for the same quantity.","PeriodicalId":54910,"journal":{"name":"Izvestiya Mathematics","volume":"85 1","pages":"351 - 366"},"PeriodicalIF":0.8,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58575362","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We employ a new approach to show that the Calderón construction for a couple of global Morrey spaces coincides with the Morrey space with appropriate parameters only under rather strong assumptions on the couples of ideal spaces that parameterize the original Morrey spaces. We show that, in the case of classical examples of global Morrey spaces, these assumptions are necessary and sufficient. Applying a well-known reduction, we use the Calderón construction for a couple of global Morrey spaces to describe the spaces given by the complex interpolation method and also to prove new interpolation theorems for global Morrey spaces.
{"title":"The Calderón construction for a couple of global Morrey spaces","authors":"E. Berezhnoi","doi":"10.1070/IM9049","DOIUrl":"https://doi.org/10.1070/IM9049","url":null,"abstract":"We employ a new approach to show that the Calderón construction for a couple of global Morrey spaces coincides with the Morrey space with appropriate parameters only under rather strong assumptions on the couples of ideal spaces that parameterize the original Morrey spaces. We show that, in the case of classical examples of global Morrey spaces, these assumptions are necessary and sufficient. Applying a well-known reduction, we use the Calderón construction for a couple of global Morrey spaces to describe the spaces given by the complex interpolation method and also to prove new interpolation theorems for global Morrey spaces.","PeriodicalId":54910,"journal":{"name":"Izvestiya Mathematics","volume":"85 1","pages":"833 - 851"},"PeriodicalIF":0.8,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58575549","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We answer a question of Filip and Tosatti concerning a basepoint-free theorem for transcendental -classes on compact Kähler threefolds.
我们回答了Filip和Tosatti关于紧Kähler三折上超越类的无基点定理的问题。
{"title":"Adjoint -classes on threefolds","authors":"A. Höring","doi":"10.1070/IM9084","DOIUrl":"https://doi.org/10.1070/IM9084","url":null,"abstract":"We answer a question of Filip and Tosatti concerning a basepoint-free theorem for transcendental -classes on compact Kähler threefolds.","PeriodicalId":54910,"journal":{"name":"Izvestiya Mathematics","volume":"85 1","pages":"823 - 830"},"PeriodicalIF":0.8,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58576577","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We find explicitly a basis for the derived group of a partially commutative metabelian group and describe a canonical representation for the elements of the group.
我们显式地找到了部分可交换亚丫群的派生群的一个基，并描述了群中元素的正则表示。
{"title":"A basis for a partially commutative metabelian group","authors":"E. Timoshenko","doi":"10.1070/IM9034","DOIUrl":"https://doi.org/10.1070/IM9034","url":null,"abstract":"We find explicitly a basis for the derived group of a partially commutative metabelian group and describe a canonical representation for the elements of the group.","PeriodicalId":54910,"journal":{"name":"Izvestiya Mathematics","volume":"85 1","pages":"813 - 822"},"PeriodicalIF":0.8,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58575193","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In the paper, we obtain order estimates for the Kolmogorov widths of the intersection of weighted Sobolev classes with conditions on the first and zeroth derivatives; the weights have power-law form.
{"title":"Kolmogorov widths of intersections of weighted Sobolev classes on an interval with conditions on the zeroth and first derivatives","authors":"A. Vasil'eva","doi":"10.1070/IM8969","DOIUrl":"https://doi.org/10.1070/IM8969","url":null,"abstract":"In the paper, we obtain order estimates for the Kolmogorov widths of the intersection of weighted Sobolev classes with conditions on the first and zeroth derivatives; the weights have power-law form.","PeriodicalId":54910,"journal":{"name":"Izvestiya Mathematics","volume":"85 1","pages":"1 - 23"},"PeriodicalIF":0.8,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58573696","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We consider an elliptic boundary-value problem with a homogeneous Dirichlet boundary condition, a parameter and a discontinuous non-linearity. The positive parameter appears as a multiplicative term in the non-linearity, and the problem has a zero solution for any value of the parameter. The non-linearity has superlinear growth at infinity. We prove the existence of positive solutions by a topological method.
{"title":"Positive solutions of superlinear elliptic problems with discontinuous non-linearities","authors":"V. Pavlenko, D. K. Potapov","doi":"10.1070/IM9000","DOIUrl":"https://doi.org/10.1070/IM9000","url":null,"abstract":"We consider an elliptic boundary-value problem with a homogeneous Dirichlet boundary condition, a parameter and a discontinuous non-linearity. The positive parameter appears as a multiplicative term in the non-linearity, and the problem has a zero solution for any value of the parameter. The non-linearity has superlinear growth at infinity. We prove the existence of positive solutions by a topological method.","PeriodicalId":54910,"journal":{"name":"Izvestiya Mathematics","volume":"85 1","pages":"262 - 278"},"PeriodicalIF":0.8,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58573892","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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