Michigan Mathematical Journal最新文献_第10页

IF 0.9 3区数学

Michigan Mathematical Journal Pub Date : 2020-07-06 DOI: 10.1307/mmj/20206021

Thomas Godland, Z. Kabluchko, D. Zaporozhets

{"title":"Angle Sums of Random Polytopes","authors":"Thomas Godland, Z. Kabluchko, D. Zaporozhets","doi":"10.1307/mmj/20206021","DOIUrl":"https://doi.org/10.1307/mmj/20206021","url":null,"abstract":"For two families of random polytopes we compute explicitly the expected sums of the conic intrinsic volumes and the Grassmann angles at all faces of any given dimension of the polytope under consideration. As special cases, we compute the expected sums of internal and external angles at all faces of any fixed dimension. The first family are the Gaussian polytopes defined as convex hulls of i.i.d. samples from a non-degenerate Gaussian distribution in $mathbb R^d$. The second family are convex hulls of random walks with exchangeable increments satisfying certain mild general position assumption. The expected sums are expressed in terms of the angles of the regular simplices and the Stirling numbers, respectively. There are non-trivial analogies between these two settings. Further, we compute the angle sums for Gaussian projections of arbitrary polyhedral sets, of which the Gaussian polytopes are a special case. Also, we show that the expected Grassmann angle sums of a random polytope with a rotationally invariant law are invariant under affine transformations. Of independent interest may be also results on the faces of linear images of polyhedral sets. These results are well known but it seems that no detailed proofs can be found in the existing literature.","PeriodicalId":49820,"journal":{"name":"Michigan Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2020-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75279802","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: 4

The Behavior at Infinity of p-Harmonic Measure in an Infinite Slab 无限平板中p谐测度在无穷远处的行为

IF 0.9 3区数学

Michigan Mathematical Journal Pub Date : 2020-06-01 DOI: 10.1307/mmj/1592877615

Dante DeBlassie, R. Smits

引用次数: 2

Twisted Mazur Pattern Satellite Knots & Bordered Floer Theory 扭曲马祖尔图案卫星结和镶边花理论

IF 0.9 3区数学

Michigan Mathematical Journal Pub Date : 2020-05-26 DOI: 10.1307/mmj/20205927

I. Petkova, Biji Wong

引用次数: 4

Finiteness of log Abundant log Canonical Pairs in log Minimal Model Program with Scaling 带缩放的对数最小模型程序中对数丰度对数典范对的有限性

IF 0.9 3区数学

Michigan Mathematical Journal Pub Date : 2020-05-25 DOI: 10.1307/mmj/20226207

K. Hashizume

引用次数: 7

Simple Supercuspidals and the Langlands Correspondence 《简单超词》和《朗兰兹通信》

IF 0.9 3区数学

Michigan Mathematical Journal Pub Date : 2020-05-18 DOI: 10.1307/mmj/20207202

B. Gross

引用次数: 0

Global Newlander–Nirenberg Theorem for Domains with C2 Boundary C2边界域的全局Newlander-Nirenberg定理

IF 0.9 3区数学

Michigan Mathematical Journal Pub Date : 2020-05-15 DOI: 10.1307/mmj/20216084

Chun Gan, Xianghong Gong

{"title":"Global Newlander–Nirenberg Theorem for Domains with C2 Boundary","authors":"Chun Gan, Xianghong Gong","doi":"10.1307/mmj/20216084","DOIUrl":"https://doi.org/10.1307/mmj/20216084","url":null,"abstract":"The Newlander-Nirenberg theorem says that a formally integrable complex structure is locally equivalent to the standard complex structure in the complex Euclidean space. In this paper, we consider two natural generalizations of the Newlander-Nirenberg theorem under the presence of a $C^2$ strictly pseudoconvex boundary. When a given formally integrable complex structure $X$ is defined on the closure of a bounded strictly pseudoconvex domain with $C^2$ boundary $Dsubset mathbb{C}^n$, we show the existence of global holomorphic coordinate systems defined on $overline{D}$ that transform $X$ into the standard complex structure provided that $X$ is sufficiently close to the standard complex structure. Moreover, we show that such closeness is stable under a small $C^2$ perturbation of $partial D$. As a consequence, when a given formally integrable complex structure is defined on a one-sided neighborhood of some point in a $C^2$ real hypersurface $Msubset mathbb{C}^n$, we prove the existence of local one-sided holomorphic coordinate systems provided that $M$ is strictly pseudoconvex with respect to the given complex structure. We also obtain results when the structures are finite smooth.","PeriodicalId":49820,"journal":{"name":"Michigan Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2020-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89764845","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: 2

Geodesic Gaussian Integer Continued Fractions 测地线高斯整数连分数

IF 0.9 3区数学

Michigan Mathematical Journal Pub Date : 2020-05-01 DOI: 10.1307/mmj/1576033219

M. Hockman

引用次数: 0

On Existence of Euclidean Ideal Classes in Real Cubic and Quadratic Fields with Cyclic Class Group 具有循环类群的实数三次和二次域欧几里得理想类的存在性

IF 0.9 3区数学

Michigan Mathematical Journal Pub Date : 2020-05-01 DOI: 10.1307/mmj/1580180457

S. Gun, J. Sivaraman

引用次数: 2

Homology Spheres Bounding Acyclic Smooth Manifolds and Symplectic Fillings 含无环光滑流形的同调球与辛填充