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A Guided Tour to Normalized Volume 规范化音量的导览
IF 1.1 2区 数学
Journal of Geometric Analysis Pub Date : 2018-06-19 DOI: 10.1007/978-3-030-34953-0_10
Chi Li, Yuchen Liu, Chenyang Xu
{"title":"A Guided Tour to Normalized Volume","authors":"Chi Li, Yuchen Liu, Chenyang Xu","doi":"10.1007/978-3-030-34953-0_10","DOIUrl":"https://doi.org/10.1007/978-3-030-34953-0_10","url":null,"abstract":"","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":"32 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2018-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83111353","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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: 42
Some Questions in the Theory of Pseudoholomorphic Curves 伪全纯曲线理论中的几个问题
IF 1.1 2区 数学
Journal of Geometric Analysis Pub Date : 2018-05-24 DOI: 10.1007/978-3-030-34953-0_24
A. Zinger
{"title":"Some Questions in the Theory of Pseudoholomorphic Curves","authors":"A. Zinger","doi":"10.1007/978-3-030-34953-0_24","DOIUrl":"https://doi.org/10.1007/978-3-030-34953-0_24","url":null,"abstract":"","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":"49 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2018-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83522151","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Singular Ricci Flows II 奇异里奇流2
IF 1.1 2区 数学
Journal of Geometric Analysis Pub Date : 2018-04-09 DOI: 10.1007/978-3-030-34953-0_8
B. Kleiner, J. Lott
{"title":"Singular Ricci Flows II","authors":"B. Kleiner, J. Lott","doi":"10.1007/978-3-030-34953-0_8","DOIUrl":"https://doi.org/10.1007/978-3-030-34953-0_8","url":null,"abstract":"","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":"11 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2018-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77222699","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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: 5
Bottom of Spectra and Amenability of Coverings 光谱底部和覆盖物的适应性
IF 1.1 2区 数学
Journal of Geometric Analysis Pub Date : 2018-03-20 DOI: 10.1007/978-3-030-34953-0_2
W. Ballmann, Henrik Matthiesen, Panagiotis Polymerakis
{"title":"Bottom of Spectra and Amenability of Coverings","authors":"W. Ballmann, Henrik Matthiesen, Panagiotis Polymerakis","doi":"10.1007/978-3-030-34953-0_2","DOIUrl":"https://doi.org/10.1007/978-3-030-34953-0_2","url":null,"abstract":"","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":"40 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2018-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91302777","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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: 5
On the Existence Problem of Einstein–Maxwell Kähler Metrics 爱因斯坦-麦克斯韦的存在性问题Kähler度量
IF 1.1 2区 数学
Journal of Geometric Analysis Pub Date : 2018-03-19 DOI: 10.1007/978-3-030-34953-0_6
A. Futaki, Hajime Ono
{"title":"On the Existence Problem of Einstein–Maxwell Kähler Metrics","authors":"A. Futaki, Hajime Ono","doi":"10.1007/978-3-030-34953-0_6","DOIUrl":"https://doi.org/10.1007/978-3-030-34953-0_6","url":null,"abstract":"","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":"10 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2018-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79955074","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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: 5
K-Semistability of cscK Manifolds with Transcendental Cohomology Class. 具有超越上同调类的cscK流形的k -半稳定性。
IF 1.1 2区 数学
Journal of Geometric Analysis Pub Date : 2018-01-01 Epub Date: 2017-10-16 DOI: 10.1007/s12220-017-9942-9
Zakarias Sjöström Dyrefelt
{"title":"K-Semistability of cscK Manifolds with Transcendental Cohomology Class.","authors":"Zakarias Sjöström Dyrefelt","doi":"10.1007/s12220-017-9942-9","DOIUrl":"https://doi.org/10.1007/s12220-017-9942-9","url":null,"abstract":"<p><p>We prove that constant scalar curvature Kähler (cscK) manifolds with transcendental cohomology class are K-semistable, naturally generalising the situation for polarised manifolds. Relying on a recent result by R. Berman, T. Darvas and C. Lu regarding properness of the K-energy, it moreover follows that cscK manifolds with discrete automorphism group are uniformly K-stable. As a main step of the proof we establish, in the general Kähler setting, a formula relating the (generalised) Donaldson-Futaki invariant to the asymptotic slope of the K-energy along weak geodesic rays.</p>","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":"28 4","pages":"2927-2960"},"PeriodicalIF":1.1,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s12220-017-9942-9","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"36822412","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 17
Gauge Theory on Projective Surfaces and Anti-self-dual Einstein Metrics in Dimension Four. 四维投影曲面的规范理论与反自对偶爱因斯坦度量。
IF 1.1 2区 数学
Journal of Geometric Analysis Pub Date : 2018-01-01 Epub Date: 2017-10-12 DOI: 10.1007/s12220-017-9934-9
Maciej Dunajski, Thomas Mettler
{"title":"Gauge Theory on Projective Surfaces and Anti-self-dual Einstein Metrics in Dimension Four.","authors":"Maciej Dunajski,&nbsp;Thomas Mettler","doi":"10.1007/s12220-017-9934-9","DOIUrl":"https://doi.org/10.1007/s12220-017-9934-9","url":null,"abstract":"<p><p>Given a projective structure on a surface <math><mi>N</mi></math> , we show how to canonically construct a neutral signature Einstein metric with non-zero scalar curvature as well as a symplectic form on the total space <i>M</i> of a certain rank 2 affine bundle <math><mrow><mi>M</mi> <mo>→</mo> <mi>N</mi></mrow> </math> . The Einstein metric has anti-self-dual conformal curvature and admits a parallel field of anti-self-dual planes. We show that locally every such metric arises from our construction unless it is conformally flat. The homogeneous Einstein metric corresponding to the flat projective structure on <math> <msup><mrow><mi>RP</mi></mrow> <mn>2</mn></msup> </math> is the non-compact real form of the Fubini-Study metric on <math><mrow><mi>M</mi> <mo>=</mo> <mi>SL</mi> <mo>(</mo> <mn>3</mn> <mo>,</mo> <mi>R</mi> <mo>)</mo> <mo>/</mo> <mi>GL</mi> <mo>(</mo> <mn>2</mn> <mo>,</mo> <mi>R</mi> <mo>)</mo></mrow> </math> . We also show how our construction relates to a certain gauge-theoretic equation introduced by Calderbank.</p>","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":"28 3","pages":"2780-2811"},"PeriodicalIF":1.1,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s12220-017-9934-9","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"37028597","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
A Polyakov Formula for Sectors. 扇区的波利亚科夫公式。
IF 1.1 2区 数学
Journal of Geometric Analysis Pub Date : 2018-01-01 Epub Date: 2017-07-05 DOI: 10.1007/s12220-017-9888-y
Clara L Aldana, Julie Rowlett
{"title":"A Polyakov Formula for Sectors.","authors":"Clara L Aldana,&nbsp;Julie Rowlett","doi":"10.1007/s12220-017-9888-y","DOIUrl":"10.1007/s12220-017-9888-y","url":null,"abstract":"<p><p>We consider finite area convex Euclidean circular sectors. We prove a variational Polyakov formula which shows how the zeta-regularized determinant of the Laplacian varies with respect to the opening angle. Varying the angle corresponds to a conformal deformation in the direction of a conformal factor with a logarithmic singularity at the origin. We compute explicitly all the contributions to this formula coming from the different parts of the sector. In the process, we obtain an explicit expression for the heat kernel on an infinite area sector using Carslaw-Sommerfeld's heat kernel. We also compute the zeta-regularized determinant of rectangular domains of unit area and prove that it is uniquely maximized by the square.</p>","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":"28 2","pages":"1773-1839"},"PeriodicalIF":1.1,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s12220-017-9888-y","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"37028900","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 11
Approaching Bilinear Multipliers via a Functional Calculus. 用泛函演算逼近双线性乘数。
IF 1.1 2区 数学
Journal of Geometric Analysis Pub Date : 2018-01-01 Epub Date: 2018-01-30 DOI: 10.1007/s12220-017-9945-6
Błażej Wróbel
{"title":"Approaching Bilinear Multipliers via a Functional Calculus.","authors":"Błażej Wróbel","doi":"10.1007/s12220-017-9945-6","DOIUrl":"https://doi.org/10.1007/s12220-017-9945-6","url":null,"abstract":"<p><p>We propose a framework for bilinear multiplier operators defined via the (bivariate) spectral theorem. Under this framework, we prove Coifman-Meyer type multiplier theorems and fractional Leibniz rules. Our theory applies to bilinear multipliers associated with the discrete Laplacian on <math> <mrow> <msup><mrow><mi>Z</mi></mrow> <mi>d</mi></msup> <mo>,</mo></mrow> </math> general bi-radial bilinear Dunkl multipliers, and to bilinear multipliers associated with the Jacobi expansions.</p>","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":"28 4","pages":"3048-3080"},"PeriodicalIF":1.1,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s12220-017-9945-6","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"36822413","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Families of Strictly Pseudoconvex Domains and Peak Functions. 严格伪凸域族与峰函数。
IF 1.1 2区 数学
Journal of Geometric Analysis Pub Date : 2018-01-01 Epub Date: 2017-09-06 DOI: 10.1007/s12220-017-9912-2
Arkadiusz Lewandowski
{"title":"Families of Strictly Pseudoconvex Domains and Peak Functions.","authors":"Arkadiusz Lewandowski","doi":"10.1007/s12220-017-9912-2","DOIUrl":"https://doi.org/10.1007/s12220-017-9912-2","url":null,"abstract":"<p><p>We prove that given a family <math><mrow><mo>(</mo> <msub><mi>G</mi> <mi>t</mi></msub> <mo>)</mo></mrow> </math> of strictly pseudoconvex domains varying in <math> <msup><mrow><mi>C</mi></mrow> <mn>2</mn></msup> </math> topology on domains, there exists a continuously varying family of peak functions <math><msub><mi>h</mi> <mrow><mi>t</mi> <mo>,</mo> <mi>ζ</mi></mrow> </msub> </math> for all <math><msub><mi>G</mi> <mi>t</mi></msub> </math> at every <math><mrow><mi>ζ</mi> <mo>∈</mo> <mi>∂</mi> <msub><mi>G</mi> <mi>t</mi></msub> </mrow> </math> .</p>","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":"28 3","pages":"2466-2476"},"PeriodicalIF":1.1,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s12220-017-9912-2","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"37028505","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
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