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Asian Journal of Mathematics最新文献

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The $L_p$ Minkowski problem for the electrostatic $mathfrak{p}$-capacity for $p gt 1$ and $mathfrak{p} geqslant n^ast$ 对于 $p gt 1$ 和 $mathfrak{p} 的静电 $mathfrak{p}$ 容量的 $L_p$ Minkowski 问题gqslant n^ast$
IF 0.6 4区 数学
Asian Journal of Mathematics Pub Date : 2024-08-07 DOI: 10.4310/ajm.2024.v28.n1.a2
Xinbao Lu, Ge Xiong, Jiawei Xiong
{"title":"The $L_p$ Minkowski problem for the electrostatic $mathfrak{p}$-capacity for $p gt 1$ and $mathfrak{p} geqslant n^ast$","authors":"Xinbao Lu, Ge Xiong, Jiawei Xiong","doi":"10.4310/ajm.2024.v28.n1.a2","DOIUrl":"https://doi.org/10.4310/ajm.2024.v28.n1.a2","url":null,"abstract":"The existence and uniqueness of solutions to the $L_p$ Minkowski problem for $mathfrak{p}$-capacity for $p gt 1$ and $mathfrak{p} geqslant n$ are proved. For this task, the estimation of $mathfrak{p}$−capacitary measure controlled below by the surface area measure is achieved. This work is a sequel to the results $href{https://doi.org/10.4310/jdg/1606964418}{[45]}$ for $p gt 1$ and $1 lt mathfrak{p} lt n$.","PeriodicalId":55452,"journal":{"name":"Asian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141968615","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
Representation formulae for the higher-order Steklov and $L^{2^m}$-Friedrichs inequalities 高阶斯特克洛夫不等式和 $L^{2^m}$ 弗里德里希不等式的表示公式
IF 0.6 4区 数学
Asian Journal of Mathematics Pub Date : 2024-08-07 DOI: 10.4310/ajm.2024.v28.n1.a4
Tohru Ozawa, Durvudkhan Suragan
{"title":"Representation formulae for the higher-order Steklov and $L^{2^m}$-Friedrichs inequalities","authors":"Tohru Ozawa, Durvudkhan Suragan","doi":"10.4310/ajm.2024.v28.n1.a4","DOIUrl":"https://doi.org/10.4310/ajm.2024.v28.n1.a4","url":null,"abstract":"In this paper, we obtain remainder term representation formulae for the higher-order Steklov inequality for vector fields which imply short and direct proofs of the sharp (classical) Steklov inequalities. The obtained results directly imply sharp Steklov type inequalities for some vector fields satisfying Hörmander’s condition, for example. We also give representation formulae for the $L^{2^m}$-Friedrichs inequalities for vector fields.","PeriodicalId":55452,"journal":{"name":"Asian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141931320","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
Hodge moduli algebras and complete invariants of singularities 霍奇模量代数和奇点的完整不变式
IF 0.6 4区 数学
Asian Journal of Mathematics Pub Date : 2024-08-07 DOI: 10.4310/ajm.2024.v28.n1.a1
Guorui Ma, Yang Wang, Stephen S.-T. Yau, Huaiqing Zuo
{"title":"Hodge moduli algebras and complete invariants of singularities","authors":"Guorui Ma, Yang Wang, Stephen S.-T. Yau, Huaiqing Zuo","doi":"10.4310/ajm.2024.v28.n1.a1","DOIUrl":"https://doi.org/10.4310/ajm.2024.v28.n1.a1","url":null,"abstract":"We introduce the Hodge moduli algebras and Hodge moduli sequence associated with an isolated hypersurface singularity. These are new subtle invariants of singularities. We propose several characterization conjectures by using of these invariants. We investigate structural properties and numerical invariants of Hodge ideals naturally associated with isolated hypersurface singularities.In particular, we establish that the analytic isomorphisms class of an isolated two dimensional rational hypersurface singularities is determined by the Hodge moduli algebras and Hodge moduli sequence. As a result, we prove that Hodge moduli algebra together with the geometric genus give complete characterization of such singularities. In the proof, we concretely compute the Hodge ideals and the associated Hodge moduli algebras of these singularities.","PeriodicalId":55452,"journal":{"name":"Asian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141931319","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
Elliptic gradient estimate for the $p$−Laplace operator on the graph 图上 $p$ 拉普拉斯算子的椭圆梯度估计
IF 0.6 4区 数学
Asian Journal of Mathematics Pub Date : 2024-08-07 DOI: 10.4310/ajm.2024.v28.n1.a3
Lin Feng Wang
{"title":"Elliptic gradient estimate for the $p$−Laplace operator on the graph","authors":"Lin Feng Wang","doi":"10.4310/ajm.2024.v28.n1.a3","DOIUrl":"https://doi.org/10.4310/ajm.2024.v28.n1.a3","url":null,"abstract":"Let $G(V,E)$ be a connected locally finite graph. In this paper we consider the elliptic gradient estimate for solutions to the equation[Delta_p u - lambda_p {lvert u rvert}^{p-2} u]on $G$ with the $mathrm{CD}^psi_p (m,-K)$ condition, where $p geq 2$, $m gt 0$, $K geq 0$, and $Delta_p$ denotes the $ptextrm{-}$Laplacian. As applications, we can derive Liouville theorems and the Harnack inequality.","PeriodicalId":55452,"journal":{"name":"Asian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141931322","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
Lefschetz number formula for Shimura varieties of Hodge type 霍奇型志村变的列夫谢茨数公式
IF 0.6 4区 数学
Asian Journal of Mathematics Pub Date : 2024-08-07 DOI: 10.4310/ajm.2024.v28.n1.a5
Dong Uk Lee
{"title":"Lefschetz number formula for Shimura varieties of Hodge type","authors":"Dong Uk Lee","doi":"10.4310/ajm.2024.v28.n1.a5","DOIUrl":"https://doi.org/10.4310/ajm.2024.v28.n1.a5","url":null,"abstract":"For any Shimura variety of Hodge type with hyperspecial level at a prime $p$ and automorphic lisse sheaf on it, we prove a formula, conjectured by Kottwitz [Kot90], for the Lefschetz numbers of Frobenius-twisted Hecke correspondences acting on the compactly supported étale cohomology. Our proof is an adaptation of the arguments of Langlands and Rapoport [LR87] of deriving the Kottwitz’s formula from their conjectural description of the set of mod-$p$ points of Shimura variety (Langlands–Rapoport conjecture), but replaces their Galois gerb theoretic arguments by more standard group-theoretic ones, using Kisin’s geometric work [Kis17]. We also prove a generalization of Honda–Tate theorem in the context of Shimura varieties and fix an error in the Kisin’s work. We do not assume that the derived group is simply connected.","PeriodicalId":55452,"journal":{"name":"Asian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141931321","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
Martin boundary theory on inhomogeneous fractals 非均质分形的马丁边界理论
IF 0.6 4区 数学
Asian Journal of Mathematics Pub Date : 2024-07-12 DOI: 10.4310/ajm.2023.v27.n5.a2
Uta Freiberg, Stefan Kohl
{"title":"Martin boundary theory on inhomogeneous fractals","authors":"Uta Freiberg, Stefan Kohl","doi":"10.4310/ajm.2023.v27.n5.a2","DOIUrl":"https://doi.org/10.4310/ajm.2023.v27.n5.a2","url":null,"abstract":"We consider fractals generated by a probabilistic iterated function scheme with open set condition and we interpret the probabilities as weights for every part of the fractal. In the homogeneous case, where the weights are not taken into account, Denker and Sato introduced in 2001 a Markov chain on the word space and proved that the Martin boundary is homeomorphic to the fractal set. Our aim is to redefine the transition probability with respect to the weights and to calculate the Martin boundary. As we will see, the inhomogeneous Martin boundary coincides with the homogeneous case.","PeriodicalId":55452,"journal":{"name":"Asian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141612983","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
Typical self-affine sets with non-empty interior 具有非空内部的典型自阿芬集合
IF 0.6 4区 数学
Asian Journal of Mathematics Pub Date : 2024-07-12 DOI: 10.4310/ajm.2023.v27.n5.a1
De-Jun Feng, Zhou Feng
{"title":"Typical self-affine sets with non-empty interior","authors":"De-Jun Feng, Zhou Feng","doi":"10.4310/ajm.2023.v27.n5.a1","DOIUrl":"https://doi.org/10.4310/ajm.2023.v27.n5.a1","url":null,"abstract":"Let $T_1, dotsc , T_m$ be a family of $d times d$ invertible real matrices with $rVert T_i rvert lt 1/2$ for $1 leq i leq m$. We provide some sufficient conditions on these matrices such that the self-affine set generated by the iterated function system $lbrace T_i x + a_i rbrace$ on $mathbb{R}^d$ has non-empty interior for almost all $(a_1 , dotsc , a_m) in mathbb{R}^{md}$.","PeriodicalId":55452,"journal":{"name":"Asian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141612984","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 weak elliptic Harnack inequality revisited 弱椭圆哈纳克不等式再探讨
IF 0.6 4区 数学
Asian Journal of Mathematics Pub Date : 2024-07-12 DOI: 10.4310/ajm.2023.v27.n5.a4
Jiaxin Hu, Zhenyu Yu
{"title":"The weak elliptic Harnack inequality revisited","authors":"Jiaxin Hu, Zhenyu Yu","doi":"10.4310/ajm.2023.v27.n5.a4","DOIUrl":"https://doi.org/10.4310/ajm.2023.v27.n5.a4","url":null,"abstract":"In this paper we firstly derive the weak elliptic Harnack inequality from the generalized capacity condition, the tail estimate of jump measure and the Poincaré inequality, for any regular Dirichlet form without killing part on a measure metric space, by using the lemma of growth and the John-Nirenberg inequality. We secondly show several equivalent characterizations of the weak elliptic Harnack inequality for any (not necessarily regular) Dirichlet form. We thirdly present some consequences of the weak elliptic Harnack inequality.","PeriodicalId":55452,"journal":{"name":"Asian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141612986","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
Off-diagonal lower estimates and Hölder regularity of the heat kernel 热核的非对角下限估计和荷尔德正则性
IF 0.6 4区 数学
Asian Journal of Mathematics Pub Date : 2024-07-12 DOI: 10.4310/ajm.2023.v27.n5.a3
Alexander Grigor’yan, Eryan Hu, Jiaxin Hu
{"title":"Off-diagonal lower estimates and Hölder regularity of the heat kernel","authors":"Alexander Grigor’yan, Eryan Hu, Jiaxin Hu","doi":"10.4310/ajm.2023.v27.n5.a3","DOIUrl":"https://doi.org/10.4310/ajm.2023.v27.n5.a3","url":null,"abstract":"We study the heat kernel of a regular symmetric Dirichlet form on a metric space with doubling measure, in particular, a connection between the properties of the jump measure and the long time behaviour of the heat kernel. Under appropriate optimal hypotheses, we obtain the Hölder regularity and lower estimates of the heat kernel.","PeriodicalId":55452,"journal":{"name":"Asian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141612985","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
Branched Cauchy–Riemann structures on once-punctured torus bundles 一次穿刺环束上的分支柯西-黎曼结构
IF 0.6 4区 数学
Asian Journal of Mathematics Pub Date : 2023-04-27 DOI: 10.4310/ajm.2022.v26.n6.a2
Alex Casella
{"title":"Branched Cauchy–Riemann structures on once-punctured torus bundles","authors":"Alex Casella","doi":"10.4310/ajm.2022.v26.n6.a2","DOIUrl":"https://doi.org/10.4310/ajm.2022.v26.n6.a2","url":null,"abstract":"Unlike in hyperbolic geometry, the monodromy ideal triangulation of a hyperbolic once-punctured torus bundle $M_f$ has no natural geometric realization in Cauchy–Riemann (CR) space. By introducing a new type of 3‑cell, we construct a different cell decomposition $mathcal{D}_f$ of $M_f$ that is always realisable in CR space. As a consequence, we show that every hyperbolic once-punctured torus bundle admits a branched CR structure, whose branch locus is contained in the union of all edges of $mathcal{D}_f$. Furthermore, we explicitly compute the ramification order around each component of the branch locus and analyse the corresponding holonomy representations.","PeriodicalId":55452,"journal":{"name":"Asian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138505773","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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