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Einstein–Klein–Gordon spacetimes in the harmonic near-Minkowski regime 调和近闵可夫斯基态中的爱因斯坦-克莱因-戈登时空
IF 0.8 4区 数学
Portugaliae Mathematica Pub Date : 2022-08-18 DOI: 10.4171/pm/2084
P. LeFloch, Yue Ma
{"title":"Einstein–Klein–Gordon spacetimes in the harmonic near-Minkowski regime","authors":"P. LeFloch, Yue Ma","doi":"10.4171/pm/2084","DOIUrl":"https://doi.org/10.4171/pm/2084","url":null,"abstract":"We study the initial value problem for the Einstein-Klein-Gordon system and establish the global nonlinear stability of massive matter in the near-Minkowski regime when the initial geometry is a perturbation of an asymptotically flat, spacelike hypersurface in Minkowski spacetime and the metric enjoys the harmonic decay 1/r (in term of a suitable distance function r at spatial infinity). Our analysis encompasses matter fields that have small energy norm and solely enjoys a slow decay at spacelike infinity. Our proof is based on the Euclidean-hyperboloidal foliation method recently introduced by the authors, and distinguishes between the decay along asymptotically hyperbolic slices and the decay along asymptotically Euclidean slices. We carefully analyze the decay of metric component at the harmonic level 1/r, especially the metric component in the direction of the light cone. In presence of such a slow-decaying matter field, we establish a global existence theory for the Einstein equations expressed as a coupled system of nonlinear wave and Klein-Gordon equations.","PeriodicalId":51269,"journal":{"name":"Portugaliae Mathematica","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47185123","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Cohomology algebra of orbit spaces of free involutions on the product of projective space and 4-sphere 投影空间与四球积上自由对合轨道空间的上同调代数
IF 0.8 4区 数学
Portugaliae Mathematica Pub Date : 2022-07-29 DOI: 10.4171/pm/2105
Ying Sun, Jianbo Wang
{"title":"Cohomology algebra of orbit spaces of free involutions on the product of projective space and 4-sphere","authors":"Ying Sun, Jianbo Wang","doi":"10.4171/pm/2105","DOIUrl":"https://doi.org/10.4171/pm/2105","url":null,"abstract":"Let $X$ be a finitistic space with the mod 2 cohomology of the product space of a projective space and a 4-sphere. Assume that $X$ admits a free involution. In this paper we study the mod 2 cohomology algebra of the quotient of $X$ by the action of the free involution and derive some consequences regarding the existence of $mathbb{Z}_2$-equivariant maps between such $X$ and an $n$-sphere.","PeriodicalId":51269,"journal":{"name":"Portugaliae Mathematica","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45871482","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 obstacle problem for noncoercive elliptic equations with variable growth and $L^1$-data 具有$L^1$-数据的变增长非强制椭圆方程的障碍问题
IF 0.8 4区 数学
Portugaliae Mathematica Pub Date : 2022-07-11 DOI: 10.4171/pm/2079
Hocine Ayadi, F. Mokhtari, Rezak Souilah
{"title":"The obstacle problem for noncoercive elliptic equations with variable growth and $L^1$-data","authors":"Hocine Ayadi, F. Mokhtari, Rezak Souilah","doi":"10.4171/pm/2079","DOIUrl":"https://doi.org/10.4171/pm/2079","url":null,"abstract":"","PeriodicalId":51269,"journal":{"name":"Portugaliae Mathematica","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41631211","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 fixed point result for mappings on the $ell_{infty}$-sum of a closed and convex set based on the degree of nondensifiability 关于闭凸集$ell_｛infty｝$-和上映射的不动点结果
IF 0.8 4区 数学
Portugaliae Mathematica Pub Date : 2022-06-30 DOI: 10.4171/pm/2081
G. García
{"title":"A fixed point result for mappings on the $ell_{infty}$-sum of a closed and convex set based on the degree of nondensifiability","authors":"G. García","doi":"10.4171/pm/2081","DOIUrl":"https://doi.org/10.4171/pm/2081","url":null,"abstract":"","PeriodicalId":51269,"journal":{"name":"Portugaliae Mathematica","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44554386","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Approximation to the classical fractals by using non-affine contraction mappings 用非仿射压缩映射逼近经典分形
IF 0.8 4区 数学
Portugaliae Mathematica Pub Date : 2022-06-14 DOI: 10.4171/pm/2078
N. Aslan, Ismail Aslan
{"title":"Approximation to the classical fractals by using non-affine contraction mappings","authors":"N. Aslan, Ismail Aslan","doi":"10.4171/pm/2078","DOIUrl":"https://doi.org/10.4171/pm/2078","url":null,"abstract":"","PeriodicalId":51269,"journal":{"name":"Portugaliae Mathematica","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46162433","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Failure of the local chain rule for the fractional variation 分数阶变化的局部链式法则失效
IF 0.8 4区 数学
Portugaliae Mathematica Pub Date : 2022-06-07 DOI: 10.4171/pm/2096
G. Comi, Giorgio Stefani
{"title":"Failure of the local chain rule for the fractional variation","authors":"G. Comi, Giorgio Stefani","doi":"10.4171/pm/2096","DOIUrl":"https://doi.org/10.4171/pm/2096","url":null,"abstract":"We prove that the local version of the chain rule cannot hold for the fractional variation defined in arXiv:1809.08575. In the case $n = 1$, we prove a stronger result, exhibiting a function $f in BV^{alpha}(mathbb{R})$ such that $|f| notin BV^{alpha}(mathbb{R})$. The failure of the local chain rule is a consequence of some surprising rigidity properties for non-negative functions with bounded fractional variation which, in turn, are derived from a fractional Hardy inequality localized to half-spaces. Our approach exploits the results of arXiv:2111.13942 and the distributional approach of the previous papers arXiv:1809.08575, arXiv:1910.13419, arXiv:2011.03928, arXiv:2109.15263. As a byproduct, we refine the fractional Hardy inequality obtained in arXiv:1611.07204, arXiv:1806.07588 and we prove a fractional version of the closely related Meyers-Ziemer trace inequality.","PeriodicalId":51269,"journal":{"name":"Portugaliae Mathematica","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44948154","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 7
Homology of weighted path complexes and directed hypergraphs 加权路径复形与有向超图的同调性
IF 0.8 4区 数学
Portugaliae Mathematica Pub Date : 2022-04-16 DOI: 10.4171/pm/2098
Y. Muranov, A. Szczepkowska, V. Vershinin
{"title":"Homology of weighted path complexes and directed hypergraphs","authors":"Y. Muranov, A. Szczepkowska, V. Vershinin","doi":"10.4171/pm/2098","DOIUrl":"https://doi.org/10.4171/pm/2098","url":null,"abstract":"We introduce the weighted path homology on the category of weigh-ted directed hypergraphs and describe conditions of homotopy invariance of weighted path homology groups. We give several examples that explain the nontriviality of the introduced notions.","PeriodicalId":51269,"journal":{"name":"Portugaliae Mathematica","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43223708","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Algebraic cycles and Fano threefolds of genus 8 8属的代数环和Fano三倍
IF 0.8 4区 数学
Portugaliae Mathematica Pub Date : 2022-01-17 DOI: 10.4171/pm/2069
Robert Laterveer
{"title":"Algebraic cycles and Fano threefolds of genus 8","authors":"Robert Laterveer","doi":"10.4171/pm/2069","DOIUrl":"https://doi.org/10.4171/pm/2069","url":null,"abstract":"We show that prime Fano threefolds $Y$ of genus 8 have a multiplicative Chow–Künneth decomposition, in the sense of Shen–Vial. As a consequence, a certain tautological subring of the Chow ring of powers of $Y$ injects into cohomology.","PeriodicalId":51269,"journal":{"name":"Portugaliae Mathematica","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138534725","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Denumerable cellular families in $mathbf{ZF}$ $mathbf｛ZF｝中的可数蜂窝族$
IF 0.8 4区 数学
Portugaliae Mathematica Pub Date : 2022-01-17 DOI: 10.4171/pm/2070
K. Keremedis, E. Wajch
{"title":"Denumerable cellular families in $mathbf{ZF}$","authors":"K. Keremedis, E. Wajch","doi":"10.4171/pm/2070","DOIUrl":"https://doi.org/10.4171/pm/2070","url":null,"abstract":"","PeriodicalId":51269,"journal":{"name":"Portugaliae Mathematica","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47355540","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Well-posedness and long time behavior for a general class of Moore–Gibson–Thompson equations with a memory 一类具有记忆的Moore-Gibson-Thompson方程的适定性和长时间行为
IF 0.8 4区 数学
Portugaliae Mathematica Pub Date : 2022-01-17 DOI: 10.4171/pm/2074
S. Nicaise, Hizia Bounadja
{"title":"Well-posedness and long time behavior for a general class of Moore–Gibson–Thompson equations with a memory","authors":"S. Nicaise, Hizia Bounadja","doi":"10.4171/pm/2074","DOIUrl":"https://doi.org/10.4171/pm/2074","url":null,"abstract":"","PeriodicalId":51269,"journal":{"name":"Portugaliae Mathematica","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48981208","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
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