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Twisted Kähler–Einstein metrics on flag varieties 旗变体上的扭曲凯勒-爱因斯坦度量
IF 1 3区 数学
Mathematische Nachrichten Pub Date : 2024-09-13 DOI: 10.1002/mana.202300553
Eder M. Correa, Lino Grama
{"title":"Twisted Kähler–Einstein metrics on flag varieties","authors":"Eder M. Correa, Lino Grama","doi":"10.1002/mana.202300553","DOIUrl":"https://doi.org/10.1002/mana.202300553","url":null,"abstract":"In this paper, we present a description of invariant twisted Kähler–Einstein (tKE) metrics on flag varieties. Additionally, we delve into the applications of the concepts utilized in proving our main result, particularly concerning the existence of the invariant twisted constant scalar curvature Kähler metrics. Moreover, we provide a precise description of the greatest Ricci lower bound for arbitrary Kähler classes on flag varieties. From this description, we establish a sequence of inequalities linked to optimal upper bounds for the volume of Kähler metrics, relying solely on tools derived from the Lie theory. Further, we illustrate our main results through various examples, encompassing full flag varieties, the projectivization of the tangent bundle of , and families of flag varieties with a Picard number 2.","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142252029","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}
引用次数: 0
Inverse initial‐value problems for time fractional diffusion equations in fractional Sobolev spaces 分数 Sobolev 空间中时间分数扩散方程的逆初值问题
IF 1 3区 数学
Mathematische Nachrichten Pub Date : 2024-09-10 DOI: 10.1002/mana.202300292
Nguyen Huy Tuan, Bao‐Ngoc Tran
{"title":"Inverse initial‐value problems for time fractional diffusion equations in fractional Sobolev spaces","authors":"Nguyen Huy Tuan, Bao‐Ngoc Tran","doi":"10.1002/mana.202300292","DOIUrl":"https://doi.org/10.1002/mana.202300292","url":null,"abstract":"We study the time fractional diffusion equation , , in a bounded domain with an elliptic operator and a locally Lipschitz nonlinearity on fractional Sobolev spaces, subjected to the homogeneous Dirichlet boundary condition. Data have not been measured at the initial time , but at a final time , that is, is given instead of . The problem is, therefore, called an inverse initial‐value problem. We first establish the well‐posedness of this problem on fractional Sobolev spaces and the regularity of the solution by assuming only the local Lipschitz continuity of . Second, an susceptible‐infected (shortly, SI) model with heterogeneity and a Navier–Stokes equation have been exemplified. Finally, a spatial ‐estimate for the solution and its gradient has been provided. The essential tools are asymptotic behaviours of Mittag–Leffler functions, fractional power spaces, fractional Sobolev spaces and embedding, weighted functional spaces, and estimates for heat semigroup.","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142176967","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}
引用次数: 0
On a family of sparse exponential sums 关于稀疏指数和族
IF 1 3区 数学
Mathematische Nachrichten Pub Date : 2024-09-10 DOI: 10.1002/mana.202300426
Moubariz Z. Garaev, Zeev Rudnick, Igor E. Shparlinski
{"title":"On a family of sparse exponential sums","authors":"Moubariz Z. Garaev, Zeev Rudnick, Igor E. Shparlinski","doi":"10.1002/mana.202300426","DOIUrl":"https://doi.org/10.1002/mana.202300426","url":null,"abstract":"We investigate exponential sums modulo primes whose phase function is a sparse polynomial, with exponents growing with the prime. In particular, such sums model those which appear in the study of the quantum cat map. While they are not amenable to treatment by algebro‐geometric methods such as Weil's bounds, Bourgain gave a nontrivial estimate for these and more general sums. In this work, we obtain explicit bounds with reasonable savings over various types of averaging. We also initiate the study of the value distribution of these sums.","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142176968","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}
引用次数: 0
On a parabolic Monge–Ampère type equation on compact almost Hermitian manifolds 关于紧凑几乎赫尔墨斯流形上的抛物蒙日-安培类型方程
IF 1 3区 数学
Mathematische Nachrichten Pub Date : 2024-09-10 DOI: 10.1002/mana.202300155
Masaya Kawamura
{"title":"On a parabolic Monge–Ampère type equation on compact almost Hermitian manifolds","authors":"Masaya Kawamura","doi":"10.1002/mana.202300155","DOIUrl":"https://doi.org/10.1002/mana.202300155","url":null,"abstract":"We investigate a parabolic Monge–Ampère type equation on compact almost Hermitian manifolds and derive a priori gradient and second‐order derivative estimates for solutions to this parabolic equation. These a priori estimates give us higher order estimates and a long‐time solution. Then, we can observe its behavior as .","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142176985","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}
引用次数: 0
Existence of solutions for critical Neumann problem with superlinear perturbation in the half‐space 半空间超线性扰动临界诺依曼问题解的存在性
IF 1 3区 数学
Mathematische Nachrichten Pub Date : 2024-09-07 DOI: 10.1002/mana.202300496
Yinbin Deng, Longge Shi, Xinyue Zhang
{"title":"Existence of solutions for critical Neumann problem with superlinear perturbation in the half‐space","authors":"Yinbin Deng, Longge Shi, Xinyue Zhang","doi":"10.1002/mana.202300496","DOIUrl":"https://doi.org/10.1002/mana.202300496","url":null,"abstract":"In this paper, we consider the existence and multiplicity of solutions for the critical Neumann problem <jats:disp-formula> </jats:disp-formula>where , , , , , is the outward unit normal vector at the boundary , is the usual critical exponent for the Sobolev embedding and is the critical exponent for the Sobolev trace embedding . By establishing an improved Pohozaev identity, we show that problem () has no nontrivial solution if . Applying the mountain pass theorem without the condition and the delicate estimates for the mountain pass level, we obtain the existence of a positive solution for all and the different values of the parameters and . Particularly, for , , , we prove that problem () has a positive solution if and only if . Moreover, the existence of multiple solutions for () is also obtained by dual variational principle for all and suitable .","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142176973","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}
引用次数: 0
The optimal polynomial decay in the extensible Timoshenko system 可扩展季莫申科系统中的最优多项式衰减
IF 1 3区 数学
Mathematische Nachrichten Pub Date : 2024-09-02 DOI: 10.1002/mana.202300331
Moncef Aouadi
{"title":"The optimal polynomial decay in the extensible Timoshenko system","authors":"Moncef Aouadi","doi":"10.1002/mana.202300331","DOIUrl":"https://doi.org/10.1002/mana.202300331","url":null,"abstract":"In this paper, we derive the equations that constitute the nonlinear mathematical model of an extensible thermoelastic Timoshenko system. The nonlinear governing equations are derived by applying the Hamilton principle to full von Kármán equations. The model takes account of the effects of extensibility, where the dissipations are entirely contributed by temperature. Based on the semigroups theory, we establish existence and uniqueness of weak and strong solutions to the derived problem. By using a resolvent criterion, developed by Borichev and Tomilov, we prove the optimality of the polynomial decay rate of the considered problem under the condition (65). Moreover, by an approach based on the Gearhart–Herbst–Prüss–Huang theorem, we show the non‐exponential stability of the same problem; but strongly stable by following a result due to Arendt–Batty. In the absence of additional mechanical dissipations, the system is often not highly stable. By adding a damping frictional function to the first equation of the nonlinear derived model with extensibility and using the multiplier method, we show that the solutions decay exponentially if Equation (85) holds.","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142176976","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}
引用次数: 0
The canonical representation of the Drinfeld curve 德林菲尔德曲线的典型表示
IF 1 3区 数学
Mathematische Nachrichten Pub Date : 2024-09-02 DOI: 10.1002/mana.202200402
Lucas Laurent, Bernhard Köck
{"title":"The canonical representation of the Drinfeld curve","authors":"Lucas Laurent, Bernhard Köck","doi":"10.1002/mana.202200402","DOIUrl":"https://doi.org/10.1002/mana.202200402","url":null,"abstract":"If is a smooth projective curve over an algebraically closed field and is a group of automorphisms of , the <jats:italic>canonical representation of</jats:italic> is given by the induced ‐linear action of on the vector space of holomorphic differentials on . Computing it is still an open problem in general when the cover is wildly ramified. In this paper, we fix a prime power , we consider the Drinfeld curve, that is, the curve given by the equation over together with its standard action by , and decompose as a direct sum of indecomposable representations of , thus solving the aforementioned problem in this case.","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142223556","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}
引用次数: 0
Monotonicities of quasi‐normed Calderón–Lozanovskiĭ spaces with applications to approximation problems 准规范 Calderón-Lozanovskiĭ 空间的单调性及其在近似问题中的应用
IF 1 3区 数学
Mathematische Nachrichten Pub Date : 2024-09-02 DOI: 10.1002/mana.202400013
Paweł Foralewski, Paweł Kolwicz
{"title":"Monotonicities of quasi‐normed Calderón–Lozanovskiĭ spaces with applications to approximation problems","authors":"Paweł Foralewski, Paweł Kolwicz","doi":"10.1002/mana.202400013","DOIUrl":"https://doi.org/10.1002/mana.202400013","url":null,"abstract":"We consider the geometric structure of quasi‐normed Calderón–Lozanovskiĭ spaces. First, we study relations between the quasi‐norm and the quasi‐modular “near zero” and “near one,” which are fundamental for the theory. With their help, we provide a precise description of the basic monotonicity properties. In comparison with the well‐known normed case, we develop a number of new techniques and methods, among which the conditions and play a crucial role. From our general results, we conclude the criteria for monotonicity properties in quasi‐normed Orlicz spaces, which are new even in this particular context. We consider both the function and the sequence case as well as we admit degenerated Orlicz functions, which provides us with a maximal class of spaces under consideration. We also discuss the applications of suitable properties to the best dominated approximation problems in quasi‐Banach lattices.","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142176864","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}
引用次数: 0
Bifurcation for indefinite‐weighted p$p$‐Laplacian problems with slightly subcritical nonlinearity 具有轻微次临界非线性的不定加权 p$p$-Laplacian 问题的分岔问题
IF 1 3区 数学
Mathematische Nachrichten Pub Date : 2024-09-02 DOI: 10.1002/mana.202400184
Mabel Cuesta, Rosa Pardo
{"title":"Bifurcation for indefinite‐weighted p$p$‐Laplacian problems with slightly subcritical nonlinearity","authors":"Mabel Cuesta, Rosa Pardo","doi":"10.1002/mana.202400184","DOIUrl":"https://doi.org/10.1002/mana.202400184","url":null,"abstract":"We study a superlinear elliptic boundary value problem involving the ‐Laplacian operator, with changing sign weights. The problem has positive solutions bifurcating from the trivial solution set at the two principal eigenvalues of the corresponding linear weighted boundary value problem.Drabek's bifurcation result applies when the nonlinearity is of power growth. We extend Drabek's bifurcation result to <jats:italic>slightly subcritical</jats:italic> nonlinearities. Compactness in this setting is a delicate issue obtained via Orlicz spaces.","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142176978","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}
引用次数: 0
The concentration–compactness principle for Orlicz spaces and applications 奥利兹空间的集中-紧密性原理及其应用
IF 1 3区 数学
Mathematische Nachrichten Pub Date : 2024-09-02 DOI: 10.1002/mana.202300469
Julián Fernández Bonder, Analía Silva
{"title":"The concentration–compactness principle for Orlicz spaces and applications","authors":"Julián Fernández Bonder, Analía Silva","doi":"10.1002/mana.202300469","DOIUrl":"https://doi.org/10.1002/mana.202300469","url":null,"abstract":"In this paper, we extend the well‐known concentration–compactness principle of P.L. Lions to Orlicz spaces. As an application, we show an existence result to some critical elliptic problem with nonstandard growth.","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142176876","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}
引用次数: 0
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