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Homology versus homotopy in rational fibrations 有理fibrations中的同胚与同胚
IF 1.2 2区 数学
Revista Matematica Iberoamericana Pub Date : 2021-07-26 DOI: 10.4171/rmi/1298
Manuel Amann
{"title":"Homology versus homotopy in rational fibrations","authors":"Manuel Amann","doi":"10.4171/rmi/1298","DOIUrl":"https://doi.org/10.4171/rmi/1298","url":null,"abstract":"","PeriodicalId":49604,"journal":{"name":"Revista Matematica Iberoamericana","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2021-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42799695","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The reconstruction theorem in quasinormed spaces 拟赋范空间中的重构定理
IF 1.2 2区 数学
Revista Matematica Iberoamericana Pub Date : 2021-07-19 DOI: 10.4171/rmi/1355
Pavel Zorin-Kranich
{"title":"The reconstruction theorem in quasinormed spaces","authors":"Pavel Zorin-Kranich","doi":"10.4171/rmi/1355","DOIUrl":"https://doi.org/10.4171/rmi/1355","url":null,"abstract":". We extend the Hairer reconstruction theorem for distributions due to Caravenna and Zambotti [CZ20] to general function spaces satisfying a translation and scaling condition. This includes Besov type spaces with exponents below 1 and Triebel–Lizorkin type spaces.","PeriodicalId":49604,"journal":{"name":"Revista Matematica Iberoamericana","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2021-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44435635","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
$C^2$ interpolation with range restriction 带范围限制的$C^2$插值
IF 1.2 2区 数学
Revista Matematica Iberoamericana Pub Date : 2021-07-17 DOI: 10.4171/rmi/1353
C. Fefferman, Fushuai Jiang, Garving K. Luli
{"title":"$C^2$ interpolation with range restriction","authors":"C. Fefferman, Fushuai Jiang, Garving K. Luli","doi":"10.4171/rmi/1353","DOIUrl":"https://doi.org/10.4171/rmi/1353","url":null,"abstract":"Given −∞ < λ < Λ < ∞, E ⊂ R finite, and f : E → [λ,Λ], how can we extend f to a C(R) function F such that λ ≤ F ≤ Λ and ‖F‖Cm(Rn) is within a constant multiple of the least possible, with the constant depending only on m and n? In this paper, we provide the solution to the problem for the case m = 2. Specifically, we construct a (parameter-dependent, nonlinear) C(R) extension operator that preserves the range [λ,Λ], and we provide an efficient algorithm to compute such an extension using O(N logN) operations, where N = #(E).","PeriodicalId":49604,"journal":{"name":"Revista Matematica Iberoamericana","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2021-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48172847","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Expansion of harmonic functions near the boundary of Dini domains Dini域边界附近调和函数的展开
IF 1.2 2区 数学
Revista Matematica Iberoamericana Pub Date : 2021-07-13 DOI: 10.4171/rmi/1380
C. Kenig, Zihui Zhao
{"title":"Expansion of harmonic functions near the boundary of Dini domains","authors":"C. Kenig, Zihui Zhao","doi":"10.4171/rmi/1380","DOIUrl":"https://doi.org/10.4171/rmi/1380","url":null,"abstract":"Let u be a harmonic function in a C-Dini domain, such that u vanishes on an open set of the boundary. We show that near every point in the open set, u can be written uniquely as the sum of a non-trivial homogeneous harmonic polynomial and an error term of higher degree (depending on the Dini parameter). In particular, this implies that u has a unique tangent function at every such point, and that the convergence rate to the tangent function can be estimated. We also study the relationship of tangent functions at nearby points in a special case.","PeriodicalId":49604,"journal":{"name":"Revista Matematica Iberoamericana","volume":"1 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2021-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70906735","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Whitney’s extension theorem and the finiteness principle for curves in the Heisenberg group 惠特尼的可拓定理和海森堡群中曲线的有限原理
IF 1.2 2区 数学
Revista Matematica Iberoamericana Pub Date : 2021-07-09 DOI: 10.4171/rmi/1339
Scott Zimmerman
{"title":"Whitney’s extension theorem and the finiteness principle for curves in the Heisenberg group","authors":"Scott Zimmerman","doi":"10.4171/rmi/1339","DOIUrl":"https://doi.org/10.4171/rmi/1339","url":null,"abstract":"Consider the sub-Riemannian Heisenberg group H. In this paper, we answer the following question: given a compact set K ⊆ R and a continuous map f : K → H, when is there a horizontal C curve F : R → H such that F |K = f? Whitney originally answered this question for real valued mappings [35], and Fefferman provided a complete answer for real valued functions defined on subsets of R [12]. We also prove a finiteness principle for C √ ω horizontal curves in the Heisenberg group in the sense of Brudnyi and Shvartsman [5].","PeriodicalId":49604,"journal":{"name":"Revista Matematica Iberoamericana","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2021-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45303691","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
The regularity problem for degenerate elliptic operators in weighted spaces 加权空间中退化椭圆算子的正则性问题
IF 1.2 2区 数学
Revista Matematica Iberoamericana Pub Date : 2021-06-28 DOI: 10.4171/rmi/1357
P. Auscher, Li Chen, J. M. Martell, Cruz Prisuelos-Arribas
{"title":"The regularity problem for degenerate elliptic operators in weighted spaces","authors":"P. Auscher, Li Chen, J. M. Martell, Cruz Prisuelos-Arribas","doi":"10.4171/rmi/1357","DOIUrl":"https://doi.org/10.4171/rmi/1357","url":null,"abstract":"We study the solvability of the regularity problem for degenerate elliptic operators in the block case for data in weighted spaces. More precisely, let Lw be a degenerate elliptic operator with degeneracy given by a fixed weight w ∈ A2(dx) in R, and consider the associated block second order degenerate elliptic problem in the upper-half space R + . We obtain non-tangential bounds for the full gradient of the solution of the block case operator given by the Poisson semigroup in terms of the gradient of the boundary data. All this is done in the spaces L(vdw) where v is a Muckenhoupt weight with respect to the underlying natural weighted space (R, wdx). We recover earlier results in the non-degenerate case (when w ≡ 1, and with or without weight v). Our strategy is also different and more direct thanks in particular to recent observations on change of angles in weighted square function estimates and non-tangential maximal functions. Our method gives as a consequence the (unweighted) L(dx)-solvability of the regularity problem for the block operator Lαu(x, t) = −|x|divx ( |x| A(x)∇xu(x, t) ) − ∂ t u(x, t) for any complex-valued uniformly elliptic matrix A and for all −ǫ < α < 2n n+2 , where ǫ depends just on the dimension and the ellipticity constants of A.","PeriodicalId":49604,"journal":{"name":"Revista Matematica Iberoamericana","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2021-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49109657","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
A McKay bijection for projectors 投影仪的McKay双射
IF 1.2 2区 数学
Revista Matematica Iberoamericana Pub Date : 2021-06-28 DOI: 10.4171/rmi/1294
G. Navarro
{"title":"A McKay bijection for projectors","authors":"G. Navarro","doi":"10.4171/rmi/1294","DOIUrl":"https://doi.org/10.4171/rmi/1294","url":null,"abstract":"","PeriodicalId":49604,"journal":{"name":"Revista Matematica Iberoamericana","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2021-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45077658","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Real semisimple Lie groups and balanced metrics 真正的半单李群和平衡度量
IF 1.2 2区 数学
Revista Matematica Iberoamericana Pub Date : 2021-06-28 DOI: 10.4171/rmi/1391
Federico Giusti, F. Podestà
{"title":"Real semisimple Lie groups and balanced metrics","authors":"Federico Giusti, F. Podestà","doi":"10.4171/rmi/1391","DOIUrl":"https://doi.org/10.4171/rmi/1391","url":null,"abstract":"Given any non-compact real simple Lie group Go of inner type and even dimension, we prove the existence of an invariant complex structure J and a Hermitian balanced metric with vanishing Chern scalar curvature on Go and on any compact quotient M = Go/Γ, with Γ a cocompact lattice. We also prove that (M, J) does not carry any pluriclosed metric, in contrast to the case of even dimensional compact Lie groups, which admit pluriclosed but not balanced metrics.","PeriodicalId":49604,"journal":{"name":"Revista Matematica Iberoamericana","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2021-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46394112","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
On stable rank of $H^infty$ on coverings of finite bordered Riemann surfaces 有限边Riemann曲面覆盖上$H^infty$的稳定秩
IF 1.2 2区 数学
Revista Matematica Iberoamericana Pub Date : 2021-06-28 DOI: 10.4171/rmi/1293
A. Brudnyi
{"title":"On stable rank of $H^infty$ on coverings of finite bordered Riemann surfaces","authors":"A. Brudnyi","doi":"10.4171/rmi/1293","DOIUrl":"https://doi.org/10.4171/rmi/1293","url":null,"abstract":"","PeriodicalId":49604,"journal":{"name":"Revista Matematica Iberoamericana","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2021-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42081422","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Uniqueness of Yudovich’s solutions to the 2D incompressible Euler equation despite the presence of sources and sinks 尽管存在源和汇，但二维不可压缩Euler方程Yudovich解的唯一性
IF 1.2 2区 数学
Revista Matematica Iberoamericana Pub Date : 2021-06-22 DOI: 10.4171/rmi/1370
Florent Noisette, F. Sueur
{"title":"Uniqueness of Yudovich’s solutions to the 2D incompressible Euler equation despite the presence of sources and sinks","authors":"Florent Noisette, F. Sueur","doi":"10.4171/rmi/1370","DOIUrl":"https://doi.org/10.4171/rmi/1370","url":null,"abstract":"In 1962, Yudovich proved the existence and uniqueness of classical solutions to the 2D incompressible Euler equations in the case where the fluid occupies a bounded domain with entering and exiting flows on some parts of the boundary. The normal velocity is prescribed on the whole boundary, as well as the entering vorticity. The uniqueness part of Yudovich’s result holds for Hölder vorticity, by contrast with his 1961 result on the case of an impermeable boundary, for which the normal velocity is prescribed as zero on the boundary, and for which the assumption that the initial vorticity is bounded was shown to be sufficient to guarantee uniqueness. Whether or not uniqueness holds as well for bounded vorticities in the case of entering and exiting flows has been left open until 2014, when Weigant and Papin succeeded to tackle the case where the domain is a rectangle. In this paper we adapt Weigant and Papin’s result to the case of a smooth domain with several internal sources and sinks.","PeriodicalId":49604,"journal":{"name":"Revista Matematica Iberoamericana","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2021-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43830268","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
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