Acta Mathematica最新文献_第4页

Correction to “On topological cyclic homology” 对“On拓扑循环同调”的更正

IF 3.7 1区数学

Acta Mathematica Pub Date : 2019-03-01 DOI: 10.4310/ACTA.2019.V222.N1.A2

T. Nikolaus, P. Scholze

引用次数: 2

Quotients of higher-dimensional Cremona groups 高维Cremona群的群

IF 3.7 1区数学

Acta Mathematica Pub Date : 2019-01-14 DOI: 10.4310/ACTA.2021.v226.n2.a1

J. Blanc, St'ephane Lamy, Susanna Zimmermann

引用次数: 26

The directed landscape 定向景观

IF 3.7 1区数学

Acta Mathematica Pub Date : 2018-12-02 DOI: 10.4310/acta.2022.v229.n2.a1

Duncan Dauvergne, Janosch Ortmann, B'alint Vir'ag

引用次数: 116

Ancient solutions to the Ricci flow in dimension $3$ 利玛窦流的古代解法（3美元）$

IF 3.7 1区数学

Acta Mathematica Pub Date : 2018-11-06 DOI: 10.4310/acta.2020.v225.n1.a1

S. Brendle

引用次数: 60

Systems of holomorphic multivalued projections on complex manifolds 复流形上的全纯多值投影系统

IF 3.7 1区数学

Acta Mathematica Pub Date : 2018-11-01 DOI: 10.4467/20843828am.18.001.9717

Kamil Drzyzga

引用次数: 0

Irreducibility of random polynomials of large degree 大次随机多项式的不可约性

IF 3.7 1区数学

Acta Mathematica Pub Date : 2018-10-31 DOI: 10.4310/ACTA.2019.v223.n2.a1

E. Breuillard, P. P. Varj'u

引用次数: 27

Ancient low-entropy flows, mean-convex neighborhoods, and uniqueness 古代低熵流、均值凸邻域和唯一性

IF 3.7 1区数学

Acta Mathematica Pub Date : 2018-10-19 DOI: 10.4310/acta.2022.v228.n2.a1

K. Choi, Robert Haslhofer, Or Hershkovits

{"title":"Ancient low-entropy flows, mean-convex neighborhoods, and uniqueness","authors":"K. Choi, Robert Haslhofer, Or Hershkovits","doi":"10.4310/acta.2022.v228.n2.a1","DOIUrl":"https://doi.org/10.4310/acta.2022.v228.n2.a1","url":null,"abstract":"In this article, we prove the mean convex neighborhood conjecture for the mean curvature flow of surfaces in $mathbb{R}^3$. Namely, if the flow has a spherical or cylindrical singularity at a space-time point $X=(x,t)$, then there exists a positive $varepsilon=varepsilon(X)>0$ such that the flow is mean convex in a space-time neighborhood of size $varepsilon$ around $X$. The major difficulty is to promote the infinitesimal information about the singularity to a conclusion of macroscopic size. In fact, we prove a more general classification result for all ancient low entropy flows that arise as potential limit flows near $X$. Namely, we prove that any ancient, unit-regular, cyclic, integral Brakke flow in $mathbb{R}^3$ with entropy at most $sqrt{2pi/e}+delta$ is either a flat plane, a round shrinking sphere, a round shrinking cylinder, a translating bowl soliton, or an ancient oval. As an application, we prove the uniqueness conjecture for mean curvature flow through spherical or cylindrical singularities. In particular, assuming Ilmanen's multiplicity one conjecture, we conclude that for embedded two-spheres the mean curvature flow through singularities is well-posed.","PeriodicalId":50895,"journal":{"name":"Acta Mathematica","volume":null,"pages":null},"PeriodicalIF":3.7,"publicationDate":"2018-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47680734","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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: 53

The special fiber of the motivic deformation of the stable homotopy category is algebraic 稳定同伦范畴运动变形的特殊纤维是代数的

IF 3.7 1区数学

Acta Mathematica Pub Date : 2018-09-25 DOI: 10.4310/acta.2021.v226.n2.a2

Bogdan Gheorghe, Guozhen Wang, Zhouli Xu

引用次数: 32

On the structure of band edges of $2$-dimensional periodic elliptic operators $2$维周期椭圆算子的带边结构

IF 3.7 1区数学

Acta Mathematica Pub Date : 2018-09-01 DOI: 10.4310/ACTA.2018.V221.N1.A2

N. Filonov, I. Kachkovskiy

引用次数: 16

An invariance principle for ergodic scale-free random environments 遍历无标度随机环境的一个不变性原理

IF 3.7 1区数学

Acta Mathematica Pub Date : 2018-07-19 DOI: 10.4310/acta.2022.v228.n2.a2

Ewain Gwynne, Jason Miller, S. Sheffield

{"title":"An invariance principle for ergodic scale-free random environments","authors":"Ewain Gwynne, Jason Miller, S. Sheffield","doi":"10.4310/acta.2022.v228.n2.a2","DOIUrl":"https://doi.org/10.4310/acta.2022.v228.n2.a2","url":null,"abstract":"There are many classical random walk in random environment results that apply to ergodic random planar environments. We extend some of these results to random environments in which the length scale varies from place to place, so that the law of the environment is in a certain sense only translation invariant modulo scaling. For our purposes, an \"environment\" consists of an infinite random planar map embedded in $mathbb C$, each of whose edges comes with a positive real conductance. Our main result is that under modest constraints (translation invariance modulo scaling together with the finiteness of a type of specific energy) a random walk in this kind of environment converges to Brownian motion modulo time parameterization in the quenched sense. \u0000Environments of the type considered here arise naturally in the study of random planar maps and Liouville quantum gravity. In fact, the results of this paper are used in separate works to prove that certain random planar maps (embedded in the plane via the so-called Tutte embedding) have scaling limits given by SLE-decorated Liouville quantum gravity, and also to provide a more explicit construction of Brownian motion on the Brownian map. However, the results of this paper are much more general and can be read independently of that program. \u0000One general consequence of our main result is that if a translation invariant (modulo scaling) random embedded planar map and its dual have finite energy per area, then they are close on large scales to a minimal energy embedding (the harmonic embedding). To establish Brownian motion convergence for an infinite energy embedding, it suffices to show that one can perturb it to make the energy finite.","PeriodicalId":50895,"journal":{"name":"Acta Mathematica","volume":null,"pages":null},"PeriodicalIF":3.7,"publicationDate":"2018-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42123975","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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: 10