Journal of Geometric Analysis最新文献

{"title":"Intrinsic Flat and Gromov-Hausdorff Convergence of Manifolds with Ricci Curvature Bounded Below.","authors":"Rostislav Matveev,&nbsp;Jacobus W Portegies","doi":"10.1007/s12220-016-9742-7","DOIUrl":"https://doi.org/10.1007/s12220-016-9742-7","url":null,"abstract":"<p><p>We show that for a noncollapsing sequence of closed, connected, oriented Riemannian manifolds with Ricci curvature bounded below and diameter bounded above, Gromov-Hausdorff convergence agrees with intrinsic flat convergence. In particular, the limiting current is essentially unique, has multiplicity one, and mass equal to the Hausdorff measure. Moreover, the limit spaces satisfy a constancy theorem.</p>","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":"27 3","pages":"1855-1873"},"PeriodicalIF":1.1,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s12220-016-9742-7","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"37028598","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}

{"title":"<ArticleTitle xmlns:ns0=\"http://www.w3.org/1998/Math/MathML\"><ns0:math><ns0:msubsup><ns0:mi>L</ns0:mi> <ns0:mi>h</ns0:mi> <ns0:mn>2</ns0:mn></ns0:msubsup> </ns0:math> -Functions in Unbounded Balanced Domains.","authors":"Peter Pflug,&nbsp;Włodzimierz Zwonek","doi":"10.1007/s12220-016-9754-3","DOIUrl":"https://doi.org/10.1007/s12220-016-9754-3","url":null,"abstract":"<p><p>We investigate problems related with the existence of square integrable holomorphic functions on (unbounded) balanced domains. In particular, we solve the problem of Wiegerinck for balanced domains in dimension two. We also give a description of <math><msubsup><mi>L</mi> <mi>h</mi> <mn>2</mn></msubsup> </math> -domains of holomorphy in the class of balanced domains and present a purely algebraic criterion for homogeneous polynomials to be square integrable in a pseudoconvex balanced domain in <math> <msup><mrow><mi>C</mi></mrow> <mn>2</mn></msup> </math> . This allows easily to decide which pseudoconvex balanced domain in <math> <msup><mrow><mi>C</mi></mrow> <mn>2</mn></msup> </math> has a positive Bergman kernel and which admits the Bergman metric.</p>","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":"27 3","pages":"2118-2130"},"PeriodicalIF":1.1,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s12220-016-9754-3","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"37028594","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}

{"title":"Worst Singularities of Plane Curves of Given Degree.","authors":"Ivan Cheltsov","doi":"10.1007/s12220-017-9762-y","DOIUrl":"https://doi.org/10.1007/s12220-017-9762-y","url":null,"abstract":"<p><p>We prove that <math> <mrow><mfrac><mn>2</mn> <mi>d</mi></mfrac> <mo>,</mo> <mfrac><mrow><mn>2</mn> <mi>d</mi> <mo>-</mo> <mn>3</mn></mrow> <msup><mrow><mo>(</mo> <mi>d</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo></mrow> <mn>2</mn></msup> </mfrac> <mo>,</mo> <mfrac><mrow><mn>2</mn> <mi>d</mi> <mo>-</mo> <mn>1</mn></mrow> <mrow><mi>d</mi> <mo>(</mo> <mi>d</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo></mrow> </mfrac> <mo>,</mo> <mfrac><mrow><mn>2</mn> <mi>d</mi> <mo>-</mo> <mn>5</mn></mrow> <mrow><msup><mi>d</mi> <mn>2</mn></msup> <mo>-</mo> <mn>3</mn> <mi>d</mi> <mo>+</mo> <mn>1</mn></mrow> </mfrac> </mrow> </math> and <math> <mfrac><mrow><mn>2</mn> <mi>d</mi> <mo>-</mo> <mn>3</mn></mrow> <mrow><mi>d</mi> <mo>(</mo> <mi>d</mi> <mo>-</mo> <mn>2</mn> <mo>)</mo></mrow> </mfrac> </math> are the smallest log canonical thresholds of reduced plane curves of degree <math><mrow><mi>d</mi> <mo>⩾</mo> <mn>3</mn></mrow> </math> , and we describe reduced plane curves of degree <i>d</i> whose log canonical thresholds are these numbers. As an application, we prove that <math> <mrow><mfrac><mn>2</mn> <mi>d</mi></mfrac> <mo>,</mo> <mfrac><mrow><mn>2</mn> <mi>d</mi> <mo>-</mo> <mn>3</mn></mrow> <msup><mrow><mo>(</mo> <mi>d</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo></mrow> <mn>2</mn></msup> </mfrac> <mo>,</mo> <mfrac><mrow><mn>2</mn> <mi>d</mi> <mo>-</mo> <mn>1</mn></mrow> <mrow><mi>d</mi> <mo>(</mo> <mi>d</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo></mrow> </mfrac> <mo>,</mo> <mfrac><mrow><mn>2</mn> <mi>d</mi> <mo>-</mo> <mn>5</mn></mrow> <mrow><msup><mi>d</mi> <mn>2</mn></msup> <mo>-</mo> <mn>3</mn> <mi>d</mi> <mo>+</mo> <mn>1</mn></mrow> </mfrac> </mrow> </math> and <math> <mfrac><mrow><mn>2</mn> <mi>d</mi> <mo>-</mo> <mn>3</mn></mrow> <mrow><mi>d</mi> <mo>(</mo> <mi>d</mi> <mo>-</mo> <mn>2</mn> <mo>)</mo></mrow> </mfrac> </math> are the smallest values of the <math><mi>α</mi></math> -invariant of Tian of smooth surfaces in <math> <msup><mrow><mi>P</mi></mrow> <mn>3</mn></msup> </math> of degree <math><mrow><mi>d</mi> <mo>⩾</mo> <mn>3</mn></mrow> </math> . We also prove that every reduced plane curve of degree <math><mrow><mi>d</mi> <mo>⩾</mo> <mn>4</mn></mrow> </math> whose log canonical threshold is smaller than <math><mfrac><mn>5</mn> <mrow><mn>2</mn> <mi>d</mi></mrow> </mfrac> </math> is GIT-unstable for the action of the group <math> <mrow><msub><mi>PGL</mi> <mn>3</mn></msub> <mrow><mo>(</mo> <mi>C</mi> <mo>)</mo></mrow> </mrow> </math> , and we describe GIT-semistable reduced plane curves with log canonical thresholds  <math><mfrac><mn>5</mn> <mrow><mn>2</mn> <mi>d</mi></mrow> </mfrac> </math> .</p>","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":"27 3","pages":"2302-2338"},"PeriodicalIF":1.1,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s12220-017-9762-y","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"37028600","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}

{"title":"Medial Axis and Singularities.","authors":"Lev Birbrair,&nbsp;Maciej P Denkowski","doi":"10.1007/s12220-017-9763-x","DOIUrl":"https://doi.org/10.1007/s12220-017-9763-x","url":null,"abstract":"<p><p>This paper is devoted to the study of the <i>medial axes</i> of sets definable in polynomially bounded o-minimal structures, i.e. the sets of points with more than one closest point with respect to the Euclidean distance. Our point of view is that of singularity theory. While trying to make the paper self-contained, we gather here also a large bunch of basic results. Our main interest, however, goes to the characterization of those singular points of a definable, closed set <math><mrow><mi>X</mi> <mo>⊂</mo> <msup><mrow><mi>R</mi></mrow> <mi>n</mi></msup> </mrow> </math> , which are reached by the medial axis.</p>","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":"27 3","pages":"2339-2380"},"PeriodicalIF":1.1,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s12220-017-9763-x","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"37029463","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}

{"title":"Injectivity and Stability for a Generic Class of Generalized Radon Transforms.","authors":"Andrew Homan,&nbsp;Hanming Zhou","doi":"10.1007/s12220-016-9729-4","DOIUrl":"https://doi.org/10.1007/s12220-016-9729-4","url":null,"abstract":"<p><p>Let (<i>M</i>, <i>g</i>) be an analytic, compact, Riemannian manifold with boundary, of dimension <math><mrow><mi>n</mi> <mo>≥</mo> <mn>2</mn></mrow> </math> . We study a class of generalized Radon transforms, integrating over a family of hypersurfaces embedded in <i>M</i>, satisfying the Bolker condition (in: Quinto, Proceedings of conference \"Seventy-five Years of Radon Transforms\", Hong Kong, 1994). Using analytic microlocal analysis, we prove a microlocal regularity theorem for generalized Radon transforms on analytic manifolds defined on an analytic family of hypersurfaces. We then show injectivity and stability for an open, dense subset of smooth generalized Radon transforms satisfying the Bolker condition, including the analytic ones.</p>","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":"27 2","pages":"1515-1529"},"PeriodicalIF":1.1,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s12220-016-9729-4","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"36847503","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}

{"title":"The Variations of Yang–Mills Lagrangian","authors":"T. Rivière","doi":"10.1007/978-3-030-34953-0_15","DOIUrl":"https://doi.org/10.1007/978-3-030-34953-0_15","url":null,"abstract":"","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":"32 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2015-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88645527","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}

{"title":"On Brunn–Minkowski-Type Inequalities for Polar Bodies","authors":"M. A. Hernández Cifre, J. Yepes Nicolás","doi":"10.1007/s12220-014-9541-y","DOIUrl":"https://doi.org/10.1007/s12220-014-9541-y","url":null,"abstract":"","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":"26 1","pages":"143 - 155"},"PeriodicalIF":1.1,"publicationDate":"2014-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s12220-014-9541-y","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"52802826","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}

{"title":"A Disc Formula for Plurisubharmonic Subextensions in Manifolds","authors":"B. Drinovec Drnovšek","doi":"10.1007/s12220-014-9474-5","DOIUrl":"https://doi.org/10.1007/s12220-014-9474-5","url":null,"abstract":"","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":"25 1","pages":"1401 - 1408"},"PeriodicalIF":1.1,"publicationDate":"2014-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s12220-014-9474-5","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"52802298","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}

{"title":"The Paley–Wiener Theorem and Limits of Symmetric Spaces","authors":"G. Ólafsson, J. Wolf","doi":"10.1007/s12220-013-9467-9","DOIUrl":"https://doi.org/10.1007/s12220-013-9467-9","url":null,"abstract":"","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":"24 1","pages":"1 - 31"},"PeriodicalIF":1.1,"publicationDate":"2013-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s12220-013-9467-9","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"52802250","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}

{"title":"Reduction of Five-Dimensional Uniformly Levi Degenerate CR Structures to Absolute Parallelisms","authors":"A. Isaev, D. Zaitsev","doi":"10.1007/s12220-013-9419-4","DOIUrl":"https://doi.org/10.1007/s12220-013-9419-4","url":null,"abstract":"","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":"23 1","pages":"1571 - 1605"},"PeriodicalIF":1.1,"publicationDate":"2013-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s12220-013-9419-4","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"52802236","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}