Advances in Geometry最新文献_第4页

Explicit p-harmonic functions on the real Grassmannians 实格拉斯曼人上的显式p调和函数

IF 0.5 4区数学

Advances in Geometry Pub Date : 2023-07-14 DOI: 10.1515/advgeom-2023-0015

Elsa Ghandour, Sigmundur Gudmundsson

引用次数: 1

Frontmatter 头版头条

4区数学

Advances in Geometry Pub Date : 2023-05-01 DOI: 10.1515/advgeom-2023-frontmatter2

引用次数: 0

Pseudoholomorphic curves on the LCS-fication of contact manifolds 接触流形LCS化上的伪全纯曲线

IF 0.5 4区数学

Advances in Geometry Pub Date : 2023-05-01 DOI: 10.1515/advgeom-2023-0004

Y. Oh, Y. Savelyev

{"title":"Pseudoholomorphic curves on the LCS-fication of contact manifolds","authors":"Y. Oh, Y. Savelyev","doi":"10.1515/advgeom-2023-0004","DOIUrl":"https://doi.org/10.1515/advgeom-2023-0004","url":null,"abstract":"Abstract For each contact diffeomorphism ϕ : (Q, ξ) → (Q, ξ) of (Q, ξ), we equip its mapping torus Mϕ with a locally conformal symplectic form of Banyaga’s type, which we call the lcs mapping torus of the contact diffeomorphism ϕ. In the present paper, we consider the product Q × S1 = Mid (corresponding to ϕ = id) and develop basic analysis of the associated J-holomorphic curve equation, which has the form ∂ ˉ π w = 0 , w ∗ λ ∘ j = f ∗ d θ $$bar{partial}^{pi} w=0, quad w^{*} lambda circ j=f^{*} d theta$$ for the map u = (w, f) : Σ˙→Q×S1$dot{Sigma} rightarrow Q times S^{1}$for a λ-compatible almost complex structure J and a punctured Riemann surface (Σ˙,j).$(dot{Sigma}, j).$In particular, w is a contact instanton in the sense of [31], [32].We develop a scheme of treating the non-vanishing charge by introducing the notion of charge class in H1(Σ˙,Z)$H^{1}(dot{Sigma}, mathbb{Z})$and develop the geometric framework for the study of pseudoholomorphic curves, a correct choice of energy and the definition of moduli spaces towards the construction of a compactification of the moduli space on the lcs-fication of (Q, λ) (more generally on arbitrary locally conformal symplectic manifolds).","PeriodicalId":7335,"journal":{"name":"Advances in Geometry","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46111720","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: 12

Mean surface and volume particle tensors under L-restricted isotropy and associated ellipsoids L-限制各向同性和相关椭球下的平均表面和体积粒子张量

IF 0.5 4区数学

Advances in Geometry Pub Date : 2023-05-01 DOI: 10.1515/advgeom-2023-0003

Rikke Eriksen, Markus Kiderlen

{"title":"Mean surface and volume particle tensors under L-restricted isotropy and associated ellipsoids","authors":"Rikke Eriksen, Markus Kiderlen","doi":"10.1515/advgeom-2023-0003","DOIUrl":"https://doi.org/10.1515/advgeom-2023-0003","url":null,"abstract":"Abstract The convex-geometric Minkowski tensors contain information about shape and orientation of the underlying convex body. They therefore yield valuable summary statistics for stationary marked point processes with marks in the family of convex bodies, or, slightly more specialised, for stationary particle processes. We show here that if the distribution of the typical particle is invariant under rotations about a fixed k-plane, then the average volume tensors of the typical particle can be derived from k + 1-dimensional sections. This finding extends the well-known three-dimensional special case to higher dimensions. A corresponding result for the surface tensors is also proven. In the last part of the paper we show how Minkowski tensors can be used to define three ellipsoidal set-valued summary statistics, discuss their estimation and illustrate their construction and use in a simulation example. Two of these, the so-called Miles ellipsoid and the inertia ellipsoid, are based on mean volume tensors of ranks up to 2. The third, based on the mean surface tensor of rank 2, will be called the Blaschke ellipsoid and is only defined when the typical particle has a rotationally symmetric distribution about an axis, as we then can use uniqueness and reconstruction results for centred ellipsoids of revolution from their rank-2 surface tensor. The latter are also established here.","PeriodicalId":7335,"journal":{"name":"Advances in Geometry","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48624995","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

Isometries of wall-connected twin buildings 连墙双栋建筑的立体图

IF 0.5 4区数学

Advances in Geometry Pub Date : 2023-03-31 DOI: 10.1515/advgeom-2023-0013

Sebastian Bischof, B. Mühlherr

引用次数: 1

Open books and embeddings of smooth and contact manifolds 光滑和接触歧管的开卷和嵌入

IF 0.5 4区数学

Advances in Geometry Pub Date : 2023-03-21 DOI: 10.1515/advgeom-2023-0008

Arijit Nath, Kuldeep Saha

引用次数: 0

Boomerang uniformity of power permutations and algebraic curves over 𝔽2n 幂置换的Boomerang一致性与上的代数曲线𝔽2n