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On Grünbaum Type Inequalities 关于<s:1> nbaum型不等式
IF 1.1 2区 数学
Journal of Geometric Analysis Pub Date : 2021-03-16 DOI: 10.1007/s12220-021-00635-y
Francisco Marín Sola, J. Yepes Nicolás
{"title":"On Grünbaum Type Inequalities","authors":"Francisco Marín Sola, J. Yepes Nicolás","doi":"10.1007/s12220-021-00635-y","DOIUrl":"https://doi.org/10.1007/s12220-021-00635-y","url":null,"abstract":"","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":"31 1","pages":"9981 - 9995"},"PeriodicalIF":1.1,"publicationDate":"2021-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s12220-021-00635-y","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"52802572","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
A Modified Morrey-Kohn-Hörmander Identity and Applications to the $$overline{partial }$$-Problem A修改Morrey-Kohn-Hörmander身份及$$overline{partial }$$的应用-问题
IF 1.1 2区 数学
Journal of Geometric Analysis Pub Date : 2021-02-27 DOI: 10.1007/S12220-021-00623-2
D. Chakrabarti, Phillip S. Harrington
{"title":"A Modified Morrey-Kohn-Hörmander Identity and Applications to the $$overline{partial }$$-Problem","authors":"D. Chakrabarti, Phillip S. Harrington","doi":"10.1007/S12220-021-00623-2","DOIUrl":"https://doi.org/10.1007/S12220-021-00623-2","url":null,"abstract":"","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":"1 1","pages":"1-38"},"PeriodicalIF":1.1,"publicationDate":"2021-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/S12220-021-00623-2","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41562911","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
The Geometry of $$Phi _S$$-Harmonic Maps $$Phi _S$$的几何-调和映射
IF 1.1 2区 数学
Journal of Geometric Analysis Pub Date : 2021-02-19 DOI: 10.1007/S12220-021-00612-5
S. Feng, Yingbo Han, Xiao Li, S. Wei
{"title":"The Geometry of $$Phi _S$$-Harmonic Maps","authors":"S. Feng, Yingbo Han, Xiao Li, S. Wei","doi":"10.1007/S12220-021-00612-5","DOIUrl":"https://doi.org/10.1007/S12220-021-00612-5","url":null,"abstract":"","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":"1 1","pages":"1-40"},"PeriodicalIF":1.1,"publicationDate":"2021-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/S12220-021-00612-5","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42941708","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: 2
Rotation Bounds for Hölder Continuous Homeomorphisms with Integrable Distortion 具有可积畸变的Hölder连续同胚的旋转界
IF 1.1 2区 数学
Journal of Geometric Analysis Pub Date : 2021-02-17 DOI: 10.1007/s12220-022-00950-y
A. Clop, L. Hitruhin, B. Sengupta
{"title":"Rotation Bounds for Hölder Continuous Homeomorphisms with Integrable Distortion","authors":"A. Clop, L. Hitruhin, B. Sengupta","doi":"10.1007/s12220-022-00950-y","DOIUrl":"https://doi.org/10.1007/s12220-022-00950-y","url":null,"abstract":"","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":"32 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2021-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44367622","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
Compactness of Surfaces in $$pmb {mathbb {R}}^n$$ with Small Total Curvature 总曲率较小的$$pmb｛mathbb｛R｝｝^n$$表面压实度
IF 1.1 2区 数学
Journal of Geometric Analysis Pub Date : 2021-02-05 DOI: 10.1007/S12220-020-00583-Z
Jianxin Sun, Jie Zhou
{"title":"Compactness of Surfaces in $$pmb {mathbb {R}}^n$$ with Small Total Curvature","authors":"Jianxin Sun, Jie Zhou","doi":"10.1007/S12220-020-00583-Z","DOIUrl":"https://doi.org/10.1007/S12220-020-00583-Z","url":null,"abstract":"","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":"1 1","pages":"1-33"},"PeriodicalIF":1.1,"publicationDate":"2021-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/S12220-020-00583-Z","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47757234","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: 0
$$C^k$$-Estimates for $$bar{partial }$$-Equation on Certain Convex Domains of Infinite Type in $$mathbb {C}^n$$ $$C^k$$无穷型凸域上的方程$$bar{partial }$$的估计 $$mathbb {C}^n$$
IF 1.1 2区 数学
Journal of Geometric Analysis Pub Date : 2021-02-01 DOI: 10.1007/S12220-019-00332-X
L. Ha
{"title":"$$C^k$$-Estimates for $$bar{partial }$$-Equation on Certain Convex Domains of Infinite Type in $$mathbb {C}^n$$","authors":"L. Ha","doi":"10.1007/S12220-019-00332-X","DOIUrl":"https://doi.org/10.1007/S12220-019-00332-X","url":null,"abstract":"","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":"402 1","pages":"2058-2087"},"PeriodicalIF":1.1,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86831125","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: 0
Nonlinear Conditions for Ultradifferentiability. 超可微性的非线性条件。
IF 1.1 2区 数学
Journal of Geometric Analysis Pub Date : 2021-01-01 Epub Date: 2021-06-19 DOI: 10.1007/s12220-021-00718-w
David Nicolas Nenning, Armin Rainer, Gerhard Schindl
{"title":"Nonlinear Conditions for Ultradifferentiability.","authors":"David Nicolas Nenning,&nbsp;Armin Rainer,&nbsp;Gerhard Schindl","doi":"10.1007/s12220-021-00718-w","DOIUrl":"https://doi.org/10.1007/s12220-021-00718-w","url":null,"abstract":"<p><p>A remarkable theorem of Joris states that a function <i>f</i> is <math><msup><mi>C</mi> <mi>∞</mi></msup> </math> if two relatively prime powers of <i>f</i> are <math><msup><mi>C</mi> <mi>∞</mi></msup> </math> . Recently, Thilliez showed that an analogous theorem holds in Denjoy-Carleman classes of Roumieu type. We prove that a division property, equivalent to Joris's result, is valid in a wide variety of ultradifferentiable classes. Generally speaking, it holds in all dimensions for non-quasianalytic classes. In the quasianalytic case we have general validity in dimension one, but we also get validity in all dimensions for certain quasianalytic classes.</p>","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":"31 12","pages":"12264-12287"},"PeriodicalIF":1.1,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s12220-021-00718-w","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"39578414","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: 3
On Finite Energy Solutions of 4-harmonic and ES-4-harmonic Maps. 关于4-调和和es -4-调和映射的有限能量解。
IF 1.1 2区 数学
Journal of Geometric Analysis Pub Date : 2021-01-01 Epub Date: 2021-02-25 DOI: 10.1007/s12220-021-00610-7
Volker Branding
{"title":"On Finite Energy Solutions of 4-harmonic and ES-4-harmonic Maps.","authors":"Volker Branding","doi":"10.1007/s12220-021-00610-7","DOIUrl":"https://doi.org/10.1007/s12220-021-00610-7","url":null,"abstract":"<p><p>4-harmonic and ES-4-harmonic maps are two generalizations of the well-studied harmonic map equation which are both given by a nonlinear elliptic partial differential equation of order eight. Due to the large number of derivatives it is very difficult to find any difference in the qualitative behavior of these two variational problems. In this article we prove that finite energy solutions of both 4-harmonic and ES-4-harmonic maps from Euclidean space must be trivial. However, the energy that we require to be finite is different for 4-harmonic and ES-4-harmonic maps pointing out a first difference between these two variational problems.</p>","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":"31 8","pages":"8666-8685"},"PeriodicalIF":1.1,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s12220-021-00610-7","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"39622726","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
Sharp Sobolev Inequalities via Projection Averages. 投影平均的尖锐Sobolev不等式。
IF 1.2 2区 数学
Journal of Geometric Analysis Pub Date : 2021-01-01 Epub Date: 2020-10-24 DOI: 10.1007/s12220-020-00544-6
Philipp Kniefacz, Franz E Schuster
{"title":"Sharp Sobolev Inequalities via Projection Averages.","authors":"Philipp Kniefacz, Franz E Schuster","doi":"10.1007/s12220-020-00544-6","DOIUrl":"10.1007/s12220-020-00544-6","url":null,"abstract":"<p><p>A family of sharp <math><msup><mi>L</mi> <mi>p</mi></msup> </math> Sobolev inequalities is established by averaging the length of <i>i</i>-dimensional projections of the gradient of a function. Moreover, it is shown that each of these new inequalities directly implies the classical <math><msup><mi>L</mi> <mi>p</mi></msup> </math>  Sobolev inequality of Aubin and Talenti and that the strongest member of this family is the only affine invariant one among them-the affine <math><msup><mi>L</mi> <mi>p</mi></msup> </math>  Sobolev inequality of Lutwak, Yang, and Zhang. When <math><mrow><mi>p</mi> <mo>=</mo> <mn>1</mn></mrow> </math> , the entire family of new Sobolev inequalities is extended to functions of bounded variation to also allow for a complete classification of all extremal functions in this case.</p>","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":"31 7","pages":"7436-7454"},"PeriodicalIF":1.2,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8549948/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"10802057","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: 0
Sharp Cheeger-Buser Type Inequalities in RCD ( K , ∞ ) Spaces. RCD (K，∞)空间中的尖锐Cheeger-Buser型不等式。
IF 1.1 2区 数学
Journal of Geometric Analysis Pub Date : 2021-01-01 Epub Date: 2020-02-14 DOI: 10.1007/s12220-020-00358-6
Nicolò De Ponti, Andrea Mondino
{"title":"<ArticleTitle xmlns:ns0=\"http://www.w3.org/1998/Math/MathML\">Sharp Cheeger-Buser Type Inequalities in <ns0:math><ns0:mrow><ns0:mi>RCD</ns0:mi> <ns0:mo>(</ns0:mo> <ns0:mi>K</ns0:mi> <ns0:mo>,</ns0:mo> <ns0:mi>∞</ns0:mi> <ns0:mo>)</ns0:mo></ns0:mrow> </ns0:math> Spaces.","authors":"Nicolò De Ponti,&nbsp;Andrea Mondino","doi":"10.1007/s12220-020-00358-6","DOIUrl":"https://doi.org/10.1007/s12220-020-00358-6","url":null,"abstract":"<p><p>The goal of the paper is to sharpen and generalise bounds involving Cheeger's isoperimetric constant <i>h</i> and the first eigenvalue <math><msub><mi>λ</mi> <mn>1</mn></msub> </math> of the Laplacian. A celebrated lower bound of <math><msub><mi>λ</mi> <mn>1</mn></msub> </math> in terms of <i>h</i>, <math> <mrow><msub><mi>λ</mi> <mn>1</mn></msub> <mo>≥</mo> <msup><mi>h</mi> <mn>2</mn></msup> <mo>/</mo> <mn>4</mn></mrow> </math> , was proved by Cheeger in 1970 for smooth Riemannian manifolds. An upper bound on <math><msub><mi>λ</mi> <mn>1</mn></msub> </math> in terms of <i>h</i> was established by Buser in 1982 (with dimensional constants) and improved (to a dimension-free estimate) by Ledoux in 2004 for smooth Riemannian manifolds with Ricci curvature bounded below. The goal of the paper is twofold. First: we sharpen the inequalities obtained by Buser and Ledoux obtaining a dimension-free sharp Buser inequality for spaces with (Bakry-Émery weighted) Ricci curvature bounded below by <math><mrow><mi>K</mi> <mo>∈</mo> <mi>R</mi></mrow> </math> (the inequality is sharp for <math><mrow><mi>K</mi> <mo>></mo> <mn>0</mn></mrow> </math> as equality is obtained on the Gaussian space). Second: all of our results hold in the higher generality of (possibly non-smooth) metric measure spaces with Ricci curvature bounded below in synthetic sense, the so-called <math><mrow><mi>RCD</mi> <mo>(</mo> <mi>K</mi> <mo>,</mo> <mi>∞</mi> <mo>)</mo></mrow> </math> spaces.</p>","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":"31 3","pages":"2416-2438"},"PeriodicalIF":1.1,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s12220-020-00358-6","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"25500442","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: 13
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