Journal of Geometric Analysis最新文献

{"title":"A Phragmén-Lindelöf Theorem via Proximate Orders, and the Propagation of Asymptotics.","authors":"Javier Jiménez-Garrido,&nbsp;Javier Sanz,&nbsp;Gerhard Schindl","doi":"10.1007/s12220-019-00203-5","DOIUrl":"https://doi.org/10.1007/s12220-019-00203-5","url":null,"abstract":"<p><p>We prove that, for asymptotically bounded holomorphic functions in a sector in <math><mrow><mi>C</mi> <mo>,</mo></mrow> </math> an asymptotic expansion in a single direction towards the vertex with constraints in terms of a logarithmically convex sequence admitting a nonzero proximate order entails asymptotic expansion in the whole sector with control in terms of the same sequence. This generalizes a result by Fruchard and Zhang for Gevrey asymptotic expansions, and the proof strongly rests on a suitably refined version of the classical Phragmén-Lindelöf theorem, here obtained for functions whose growth in a sector is specified by a nonzero proximate order in the sense of Lindelöf and Valiron.</p>","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s12220-019-00203-5","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"38553057","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":"Ultradifferentiable CR Manifolds.","authors":"Stefan Fürdös","doi":"10.1007/s12220-019-00191-6","DOIUrl":"https://doi.org/10.1007/s12220-019-00191-6","url":null,"abstract":"<p><p>In this article, the notion of ultradifferentiable CR manifold is introduced and an ultradifferentiable regularity result for finitely nondegenerate CR mappings is proven. Here, ultradifferentiable means with respect to Denjoy-Carleman classes defined by weight sequences. Furthermore, the regularity of infinitesimal CR automorphisms on ultradifferentiable abstract CR manifolds is investigated.</p>","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s12220-019-00191-6","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"38118322","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":"Pseudo-Hermitian Geometry in 3D","authors":"Paul Yang","doi":"10.1007/978-3-030-53725-8_4","DOIUrl":"https://doi.org/10.1007/978-3-030-53725-8_4","url":null,"abstract":"","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80685667","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":"$${mathbf {L}}^{{mathbf {p}}}$$-Sobolev Estimates for a Class of Integral Operators with Folding Canonical Relations","authors":"M. Pramanik, A. Seeger","doi":"10.1007/s12220-020-00388-0","DOIUrl":"https://doi.org/10.1007/s12220-020-00388-0","url":null,"abstract":"","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2019-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s12220-020-00388-0","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47311598","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":"Fourier–Mukai Transforms, Euler–Green Currents, and K-Stability","authors":"S. Paul, Kyriakos Sergiou","doi":"10.1007/978-3-030-34953-0_14","DOIUrl":"https://doi.org/10.1007/978-3-030-34953-0_14","url":null,"abstract":"","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2019-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88743174","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":"Ricci Flow and Ricci Limit Spaces","authors":"P. Topping","doi":"10.1007/978-3-030-53725-8_3","DOIUrl":"https://doi.org/10.1007/978-3-030-53725-8_3","url":null,"abstract":"","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2019-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80169392","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":"Towards a Liouville Theorem for Continuous Viscosity Solutions to Fully Nonlinear Elliptic Equations in Conformal Geometry","authors":"Yanyan Li, Luc Nguyen, Bo Wang","doi":"10.1007/978-3-030-34953-0_11","DOIUrl":"https://doi.org/10.1007/978-3-030-34953-0_11","url":null,"abstract":"","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2019-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74025078","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":"Holomorphic Sectional Curvature of Complex Finsler Manifolds.","authors":"Xueyuan Wan","doi":"10.1007/s12220-018-9985-6","DOIUrl":"https://doi.org/10.1007/s12220-018-9985-6","url":null,"abstract":"<p><p>In this paper, we get an inequality in terms of holomorphic sectional curvature of complex Finsler metrics. As applications, we prove a Schwarz Lemma from a complete Riemannian manifold to a complex Finsler manifold. We also show that a strongly pseudoconvex complex Finsler manifold with semi-positive but not identically zero holomorphic sectional curvature has negative Kodaira dimension under an extra condition.</p>","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s12220-018-9985-6","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"36945698","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\">Weak and Strong Type <ns0:math><ns0:msub><ns0:mi>A</ns0:mi> <ns0:mn>1</ns0:mn></ns0:msub> </ns0:math> - <ns0:math><ns0:msub><ns0:mi>A</ns0:mi> <ns0:mi>∞</ns0:mi></ns0:msub> </ns0:math> Estimates for Sparsely Dominated Operators.","authors":"Dorothee Frey,&nbsp;Zoe Nieraeth","doi":"10.1007/s12220-018-9989-2","DOIUrl":"https://doi.org/10.1007/s12220-018-9989-2","url":null,"abstract":"<p><p>We consider operators <i>T</i> satisfying a sparse domination property <dispformula> <math> <mrow> <mtable> <mtr> <mtd> <mrow><mrow><mo>|</mo> <mrow><mo>⟨</mo> <mi>T</mi> <mi>f</mi> <mo>,</mo> <mi>g</mi> <mo>⟩</mo></mrow> <mo>|</mo></mrow> <mo>≤</mo> <mi>c</mi> <munder><mo>∑</mo> <mrow><mi>Q</mi> <mo>∈</mo> <mi>S</mi></mrow> </munder> <msub><mrow><mo>⟨</mo> <mi>f</mi> <mo>⟩</mo></mrow> <mrow><msub><mi>p</mi> <mn>0</mn></msub> <mo>,</mo> <mi>Q</mi></mrow> </msub> <msub><mrow><mo>⟨</mo> <mi>g</mi> <mo>⟩</mo></mrow> <mrow><msubsup><mi>q</mi> <mn>0</mn> <mo>'</mo></msubsup> <mo>,</mo> <mi>Q</mi></mrow> </msub> <mrow><mo>|</mo> <mi>Q</mi> <mo>|</mo></mrow> </mrow> </mtd> </mtr> </mtable> </mrow> </math> </dispformula> with averaging exponents <math><mrow><mn>1</mn> <mo>≤</mo> <msub><mi>p</mi> <mn>0</mn></msub> <mo><</mo> <msub><mi>q</mi> <mn>0</mn></msub> <mo>≤</mo> <mi>∞</mi></mrow> </math> . We prove weighted strong type boundedness for <math> <mrow><msub><mi>p</mi> <mn>0</mn></msub> <mo><</mo> <mi>p</mi> <mo><</mo> <msub><mi>q</mi> <mn>0</mn></msub> </mrow> </math> and use new techniques to prove weighted weak type <math><mrow><mo>(</mo> <msub><mi>p</mi> <mn>0</mn></msub> <mo>,</mo> <msub><mi>p</mi> <mn>0</mn></msub> <mo>)</mo></mrow> </math> boundedness with quantitative mixed <math><msub><mi>A</mi> <mn>1</mn></msub> </math> - <math><msub><mi>A</mi> <mi>∞</mi></msub> </math> estimates, generalizing results of Lerner, Ombrosi, and Pérez and Hytönen and Pérez. Even in the case <math> <mrow><msub><mi>p</mi> <mn>0</mn></msub> <mo>=</mo> <mn>1</mn></mrow> </math> we improve upon their results as we do not make use of a Hörmander condition of the operator <i>T</i>. Moreover, we also establish a dual weak type <math><mrow><mo>(</mo> <msubsup><mi>q</mi> <mn>0</mn> <mo>'</mo></msubsup> <mo>,</mo> <msubsup><mi>q</mi> <mn>0</mn> <mo>'</mo></msubsup> <mo>)</mo></mrow> </math> estimate. In a last part, we give a result on the optimality of the weighted strong type bounds including those previously obtained by Bernicot, Frey, and Petermichl.</p>","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s12220-018-9989-2","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"36945699","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":"Big and Nef Classes, Futaki Invariant and Resolutions of Cubic Threefolds","authors":"C. Arezzo, A. D. Vedova","doi":"10.1007/978-3-030-34953-0_1","DOIUrl":"https://doi.org/10.1007/978-3-030-34953-0_1","url":null,"abstract":"","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2018-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75092447","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}