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The Bruce-Roberts number of holomorphic 1-forms along complex analytic varieties 沿复解析变体的全形 1 形的布鲁斯-罗伯茨数
arXiv - MATH - Complex Variables Pub Date : 2024-09-02 DOI: arxiv-2409.01237
Pedro Barbosa, Arturo Fernández-Pérez, Víctor León
{"title":"The Bruce-Roberts number of holomorphic 1-forms along complex analytic varieties","authors":"Pedro Barbosa, Arturo Fernández-Pérez, Víctor León","doi":"arxiv-2409.01237","DOIUrl":"https://doi.org/arxiv-2409.01237","url":null,"abstract":"We introduce the notion of the textit{Bruce-Roberts number} for holomorphic\u00001-forms relative to complex analytic varieties. Our main result shows that the\u0000Bruce-Roberts number of a 1-form $omega$ with respect to a complex analytic\u0000hypersurface $X$ with an isolated singularity can be expressed in terms of the\u0000textit{Ebeling--Gusein-Zade index} of $omega$ along $X$, the textit{Milnor\u0000number} of $omega$ and the textit{Tjurina number} of $X$. This result allows\u0000us to recover known formulas for the Bruce-Roberts number of a holomorphic\u0000function along $X$ and to establish connections between this number, the radial\u0000index, and the local Euler obstruction of $omega$ along $X$. Moreover, we\u0000present applications to both global and local holomorphic foliations in complex\u0000dimension two.","PeriodicalId":501142,"journal":{"name":"arXiv - MATH - Complex Variables","volume":"6 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142201824","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Carleson measures on domains in Heisenberg groups 海森堡群域上的卡列森度量
arXiv - MATH - Complex Variables Pub Date : 2024-09-02 DOI: arxiv-2409.01096
Tomasz Adamowicz, Marcin Gryszówka
{"title":"Carleson measures on domains in Heisenberg groups","authors":"Tomasz Adamowicz, Marcin Gryszówka","doi":"arxiv-2409.01096","DOIUrl":"https://doi.org/arxiv-2409.01096","url":null,"abstract":"We study the Carleson measures on NTA and ADP domains in the Heisenberg\u0000groups $mathbb{H}^n$ and provide two characterizations of such measures: (1)\u0000in terms of the level sets of subelliptic harmonic functions and (2) via the\u0000$1$-quasiconformal family of mappings on the Kor'anyi--Reimann unit ball.\u0000Moreover, we establish the $L^2$-bounds for the square function $S_{alpha}$ of\u0000a subelliptic harmonic function and the Carleson measure estimates for the BMO\u0000boundary data, both on NTA domains in $mathbb{H}^n$. Finally, we prove a\u0000Fatou-type theorem on $(epsilon, delta)$-domains in $mathbb{H}^n$.","PeriodicalId":501142,"journal":{"name":"arXiv - MATH - Complex Variables","volume":"41 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142201852","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Vector bundles on blown-up Hopf surfaces 吹胀的霍普夫曲面上的向量束
arXiv - MATH - Complex Variables Pub Date : 2024-08-30 DOI: arxiv-2408.17330
Matei Toma
{"title":"Vector bundles on blown-up Hopf surfaces","authors":"Matei Toma","doi":"arxiv-2408.17330","DOIUrl":"https://doi.org/arxiv-2408.17330","url":null,"abstract":"We show that certain moduli spaces of vector bundles over blown-up primary\u0000Hopf surfaces admit no compact components. These are the moduli spaces used by\u0000Andrei Teleman in his work on the classification of class $VII$ surfaces.","PeriodicalId":501142,"journal":{"name":"arXiv - MATH - Complex Variables","volume":"89 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142201854","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
$overline{partial}$-Estimates on the product of bounded Lipschitz domain $overline{partial}$-有界 Lipschitz 域乘积的估计值
arXiv - MATH - Complex Variables Pub Date : 2024-08-30 DOI: arxiv-2409.00293
Song-Ying Li, Sujuan Long, Jie Lao
{"title":"$overline{partial}$-Estimates on the product of bounded Lipschitz domain","authors":"Song-Ying Li, Sujuan Long, Jie Lao","doi":"arxiv-2409.00293","DOIUrl":"https://doi.org/arxiv-2409.00293","url":null,"abstract":"Let $D$ be a bounded domain in the complex plane with Lipschitz boundary. In\u0000the paper, we construct an integral solution operator $T[f]$ for any\u0000$overline{partial}$ closed $(0,1)$-form $fin L^p_{(0,1)}(D^n)$ solving the\u0000Cauchy-Riemain equation $overline{partial} u=f$ on the product domains $D^n$\u0000and obtain the $L^p$-estimates for all $1<ple infty$.","PeriodicalId":501142,"journal":{"name":"arXiv - MATH - Complex Variables","volume":"178 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142201860","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On Hollenbeck-Verbitsky conjecture for $4/3 < p < 2$ 关于 $4/3 < p < 2$ 的霍伦贝克-韦尔比茨基猜想
arXiv - MATH - Complex Variables Pub Date : 2024-08-30 DOI: arxiv-2408.17093
Vladan Jaguzović
{"title":"On Hollenbeck-Verbitsky conjecture for $4/3 < p < 2$","authors":"Vladan Jaguzović","doi":"arxiv-2408.17093","DOIUrl":"https://doi.org/arxiv-2408.17093","url":null,"abstract":"Let (P_+) be the Riesz's projection operator and let (P_-=I-P_+.) We find\u0000best estimates of the expression (leftlVert left( leftlvert P_+f\u0000rightrvert ^s + leftlvert P_-f rightrvert ^s right) ^{1/s} rightrVert\u0000_p ) in terms of Lebesgue p-norm of the function (f in L^p(mathbf{T})) for\u0000(p in (4/3,2)) and (0 < s leq frac{p}{p-1},) thus extending results from\u0000cite{Melentijevic_2022} and cite{Melentijevic_2023}, where the mentioned\u0000range is not considered.","PeriodicalId":501142,"journal":{"name":"arXiv - MATH - Complex Variables","volume":"2 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142201853","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Localization of zeros of polar polynomials on the unit disc 单位圆盘上极坐标多项式零点的定位
arXiv - MATH - Complex Variables Pub Date : 2024-08-30 DOI: arxiv-2409.00156
Roberto S. Costas-Santos, Abdelhamid Rehouma
{"title":"Localization of zeros of polar polynomials on the unit disc","authors":"Roberto S. Costas-Santos, Abdelhamid Rehouma","doi":"arxiv-2409.00156","DOIUrl":"https://doi.org/arxiv-2409.00156","url":null,"abstract":"We derive a useful result about the zeros of the $k$-polar polynomials on the\u0000unit circle; in particular we obtain a ring shaped region containing all the\u0000zeros of these polynomials. Some examples are presented.","PeriodicalId":501142,"journal":{"name":"arXiv - MATH - Complex Variables","volume":"72 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142201850","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the cohomologically trivial automorphisms of elliptic surfaces I: $χ(S)=0$ 论椭圆曲面的同调琐碎自形 I：$χ(S)=0$
arXiv - MATH - Complex Variables Pub Date : 2024-08-29 DOI: arxiv-2408.16936
Fabrizio CataneseBayreuth and KIAS Seoul, Davide FrapportiPolitecnico Milano, Christian GleissnerBayreuth, Wenfei LiuXiamen, Matthias SuchüttHannover
{"title":"On the cohomologically trivial automorphisms of elliptic surfaces I: $χ(S)=0$","authors":"Fabrizio CataneseBayreuth and KIAS Seoul, Davide FrapportiPolitecnico Milano, Christian GleissnerBayreuth, Wenfei LiuXiamen, Matthias SuchüttHannover","doi":"arxiv-2408.16936","DOIUrl":"https://doi.org/arxiv-2408.16936","url":null,"abstract":"In this first part we describe the group $Aut_{mathbb{Z}}(S)$ of\u0000cohomologically trivial automorphisms of a properly elliptic surface (a minimal\u0000surface $S$ with Kodaira dimension $kappa(S)=1$), in the initial case $\u0000chi(mathcal{O}_S) =0$. In particular, in the case where $Aut_{mathbb{Z}}(S)$ is finite, we give the\u0000upper bound 4 for its cardinality, showing more precisely that if\u0000$Aut_{mathbb{Z}}(S)$ is nontrivial, it is one of the following groups:\u0000$mathbb{Z}/2, mathbb{Z}/3, (mathbb{Z}/2)^2$. We also show with easy examples\u0000that the groups $mathbb{Z}/2, mathbb{Z}/3$ do effectively occur. Respectively, in the case where $Aut_{mathbb{Z}}(S)$ is infinite, we give\u0000the sharp upper bound 2 for the number of its connected components.","PeriodicalId":501142,"journal":{"name":"arXiv - MATH - Complex Variables","volume":"9 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142201855","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A remark on Bergman kernels and minimal $L^2$ integrals 关于伯格曼核和最小 $L^2$ 积分的评论
arXiv - MATH - Complex Variables Pub Date : 2024-08-29 DOI: arxiv-2408.16372
Shijie Bao, Qi'an Guan
{"title":"A remark on Bergman kernels and minimal $L^2$ integrals","authors":"Shijie Bao, Qi'an Guan","doi":"arxiv-2408.16372","DOIUrl":"https://doi.org/arxiv-2408.16372","url":null,"abstract":"In this note, we prove that one can use the generalized Bergman kernels to\u0000approximate the minimal $L^2$ integrals with respect to ideals of the ring of\u0000germs of holomorhpic functions.","PeriodicalId":501142,"journal":{"name":"arXiv - MATH - Complex Variables","volume":"93 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142201859","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Sharp radius of concavity for certain classes of analytic functions 某类解析函数的锐凹半径
arXiv - MATH - Complex Variables Pub Date : 2024-08-28 DOI: arxiv-2408.15544
Molla Basir Ahamed, Rajesh Hossain
{"title":"Sharp radius of concavity for certain classes of analytic functions","authors":"Molla Basir Ahamed, Rajesh Hossain","doi":"arxiv-2408.15544","DOIUrl":"https://doi.org/arxiv-2408.15544","url":null,"abstract":"Let $mathcal{A}$ be the class of all analytic functions $f$ defined on the\u0000open unit disk $mathbb{D}$ with the normalization $f(0)=0=f^{prime}(0)-1$.\u0000This paper examines the radius of concavity for various subclasses of\u0000$mathcal{A}$, namely $mathcal{S}_0^{(n)}$, $mathcal{K(alpha,beta)}$,\u0000$mathcal{tilde{S^*}(beta)}$, and $mathcal{S}^*(alpha)$. It also presents\u0000results for various classes of analytic functions on the unit disk. All the\u0000radii are best possible.","PeriodicalId":501142,"journal":{"name":"arXiv - MATH - Complex Variables","volume":"21 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142201856","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Sharp Bohr radius involving Schwarz functions for certain classes of analytic functions 涉及某些类解析函数的施瓦茨函数的夏普玻尔半径
arXiv - MATH - Complex Variables Pub Date : 2024-08-27 DOI: arxiv-2408.14773
Molla Basir Ahamed, Partha Pratim Roy
{"title":"Sharp Bohr radius involving Schwarz functions for certain classes of analytic functions","authors":"Molla Basir Ahamed, Partha Pratim Roy","doi":"arxiv-2408.14773","DOIUrl":"https://doi.org/arxiv-2408.14773","url":null,"abstract":"The Bohr radius for an arbitrary class $mathcal{F}$ of analytic functions of\u0000the form $f(z)=sum_{n=0}^{infty}a_nz^n$ on the unit disk\u0000$mathbb{D}={zinmathbb{C} : |z|<1}$ is the largest radius $R_{mathcal{F}}$\u0000such that every function $finmathcal{F}$ satisfies the inequality\u0000begin{align*} dleft(sum_{n=0}^{infty}|a_nz^n|,\u0000|f(0)|right)=sum_{n=1}^{infty}|a_nz^n|leq d(f(0), partial f(mathbb{D})),\u0000end{align*} for all $|z|=rleq R_{mathcal{F}}$ , where $d(0, partial\u0000f(mathbb{D}))$ is the Euclidean distance. In this paper, our aim is to\u0000determine the sharp improved Bohr radius for the classes of analytic functions\u0000$f$ satisfying differential subordination relation $zf^{prime}(z)/f(z)prec\u0000h(z)$ and $f(z)+beta zf^{prime}(z)+gamma z^2f^{primeprime}(z)prec h(z)$,\u0000where $h$ is the Janowski function. We show that improved Bohr radius can be\u0000obtained for Janowski functions as root of an equation involving Bessel\u0000function of first kind. Analogues results are obtained in this paper for\u0000$alpha$-convex functions and typically real functions, respectively. All\u0000obtained results in the paper are sharp and are improved version of [{Bull.\u0000Malays. Math. Sci. Soc.} (2021) 44:1771-1785].","PeriodicalId":501142,"journal":{"name":"arXiv - MATH - Complex Variables","volume":"729 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142201858","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","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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