Mathematische Annalen最新文献

{"title":"A sharp Hörmander estimate for multi-parameter and multi-linear Fourier multiplier operators","authors":"Jiao Chen, Danqing He, Guozhen Lu, Bae Jun Park, Lu Zhang","doi":"10.1007/s00208-024-02893-x","DOIUrl":"https://doi.org/10.1007/s00208-024-02893-x","url":null,"abstract":"<p>In this paper, we investigate the Hörmander type theorems for the multi-linear and multi-parameter Fourier multipliers. When the multipliers are characterized by <span>(L^u)</span>-based Sobolev norms for <span>(1&lt;ule 2)</span>, our results on the smoothness assumptions are sharp in the multi-parameter and bilinear case. In the multi-parameter and multi-linear case, our results are almost sharp. Moreover, even in the one-parameter and multi-linear case, our results improve earlier ones in the literature.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"46 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141192564","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":"Trends in Maxillomandibular Fixation Technique at a Single Academic Institution.","authors":"Heather Schopper, Natalie A Krane, Kevin J Sykes, Katherine Yu, J David Kriet, Clinton D Humphrey","doi":"10.1177/19433875231176339","DOIUrl":"10.1177/19433875231176339","url":null,"abstract":"<p><strong>Study design: </strong>Retrospective chart review.</p><p><strong>Objective: </strong>Restoration of premorbid occlusion is a key goal in the treatment of mandibular fractures. Placement of the patient in maxillomandibular fixation (MMF) is performed during mandibular fracture repair to help establish occlusion. A number of techniques are available to achieve MMF. We sought to examine trends in MMF technique at our institution.</p><p><strong>Methods: </strong>A retrospective chart review was conducted to evaluate patients who underwent surgical treatment of mandibular fractures between January 1, 2011 and March 31, 2021. Data including fracture characteristics, mechanism of injury, patient demographics, complication rates, and MMF technique utilized were collected.</p><p><strong>Results: </strong>One hundred sixty-three patients underwent MMF (132 males). The most common etiology of fracture was assault (34%). There was an increasing preference for rapid MMF techniques over time, as opposed to standard Erich arch bars. No significant difference in obtaining adequate fracture reduction as determined by postoperative imaging or complications were noted between those who underwent MMF with newer rapid techniques vs traditional MMF techniques.</p><p><strong>Conclusions: </strong>Our institution has demonstrated changing trends in the technique utilized for establishing occlusion intraoperatively, more recently favoring rapid MMF techniques, with similar rates of complications and ability to adequately reduce fractures.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"381 1","pages":"119-123"},"PeriodicalIF":1.3,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11107819/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90684266","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":"Higher order boundary Schauder estimates in Carnot groups","authors":"Agnid Banerjee, Nicola Garofalo, Isidro H. Munive","doi":"10.1007/s00208-024-02901-0","DOIUrl":"https://doi.org/10.1007/s00208-024-02901-0","url":null,"abstract":"<p>In his seminal 1981 study D. Jerison showed the remarkable negative phenomenon that there exist, in general, no Schauder estimates near the characteristic boundary in the Heisenberg group <span>(mathbb {H}^{n}.)</span> On the positive side, by adapting tools from Fourier and microlocal analysis, he developed a Schauder theory at a non-characteristic portion of the boundary, based on the non-isotropic Folland–Stein Hölder classes. On the other hand, the 1976 celebrated work of Rothschild and Stein on their lifting theorem established the central position of stratified nilpotent Lie groups (nowadays known as Carnot groups) in the analysis of Hörmander operators but, to present date, there exists no known counterpart of Jerison’s results in these sub-Riemannian ambients. In this paper we fill this gap. We prove optimal <span>(Gamma ^{k,alpha })</span> <span>((kge 2))</span> Schauder estimates near a <span>(C^{k,alpha })</span> non-characteristic portion of the boundary for <span>(Gamma ^{k-2, alpha })</span> perturbations of horizontal Laplacians in Carnot groups.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"95 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141192565","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 non-compact convex hull in generalized non-positive curvature","authors":"Giuliano Basso, Yannick Krifka, Elefterios Soultanis","doi":"10.1007/s00208-024-02905-w","DOIUrl":"https://doi.org/10.1007/s00208-024-02905-w","url":null,"abstract":"<p>Gromov’s (open) question whether the closed convex hull of finitely many points in a complete <span>({{,textrm{CAT},}}(0))</span> space is compact naturally extends to weaker notions of non-positive curvature in metric spaces. In this article, we consider metric spaces admitting a conical geodesic bicombing, and show that the question has a negative answer in this setting. Specifically, for each <span>(n&gt;1)</span>, we construct a complete metric space <i>X</i> admitting a conical geodesic bicombing, which is the closed convex hull of <i>n</i> points and is not compact. The space <i>X</i> moreover has the universal property that for any <i>n</i> points <span>(A={x_1,ldots ,x_n}subset Y)</span> in a complete <span>({{,textrm{CAT},}}(0))</span> space <i>Y</i> there exists a Lipschitz map <span>(f:Xrightarrow Y)</span> such that the convex hull of <span>(A)</span> is contained in <i>f</i>(<i>X</i>).</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"87 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141192661","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":"Geography of surface bundles over surfaces","authors":"R. İ. Nanç Baykur, Mustafa Korkmaz","doi":"10.1007/s00208-024-02899-5","DOIUrl":"https://doi.org/10.1007/s00208-024-02899-5","url":null,"abstract":"<p>We construct symplectic surface bundles over surfaces with positive signatures for all but 19 possible pairs of fiber and base genera. Meanwhile, we determine the commutator lengths of a few new mapping classes.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"50 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141192629","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":"From valuations on convex bodies to convex functions","authors":"Jonas Knoerr, Jacopo Ulivelli","doi":"10.1007/s00208-024-02902-z","DOIUrl":"https://doi.org/10.1007/s00208-024-02902-z","url":null,"abstract":"<p>A geometric framework relating valuations on convex bodies to valuations on convex functions is introduced. It is shown that a classical result by McMullen can be used to obtain a characterization of continuous, epi-translation invariant, and <i>n</i>-epi-homogeneous valuations on convex functions, which was previously established by Colesanti, Ludwig, and Mussnig. Following an approach by Goodey and Weil, a new characterization of 1-epi-homogeneous valuations is obtained.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"43 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141192638","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":"Eventual concavity properties of the heat flow","authors":"Kazuhiro Ishige","doi":"10.1007/s00208-024-02896-8","DOIUrl":"https://doi.org/10.1007/s00208-024-02896-8","url":null,"abstract":"<p>The eventual concavity properties are useful to characterize geometric properties of the final state of solutions to parabolic equations. In this paper we give characterizations of the eventual concavity properties of the heat flow for nonnegative, bounded measurable initial functions with compact support.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"13 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141173178","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":"Existence and nonexistence of solutions for the mean curvature equation with weights","authors":"Roberta Filippucci, Yadong Zheng","doi":"10.1007/s00208-024-02900-1","DOIUrl":"https://doi.org/10.1007/s00208-024-02900-1","url":null,"abstract":"<p>In this paper we study existence and nonexistence of positive radial solutions of a Dirichlet problem for the prescribed mean curvature operator with weights in a ball with a suitable radius. Because of the presence of different weights, possibly singular or degenerate, the problem under consideration appears rather delicate, it requires an accurate qualitative analysis of the solutions, as well as the use of Liouville type results based on an appropriate Pohozaev type identity. In addition, sufficient conditions for global solutions to be oscillatory are given.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"49 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141170383","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":"Multipliers on bi-parameter Haar system Hardy spaces","authors":"R. Lechner, P. Motakis, P. F. X. Müller, Th. Schlumprecht","doi":"10.1007/s00208-024-02887-9","DOIUrl":"https://doi.org/10.1007/s00208-024-02887-9","url":null,"abstract":"<p>Let <span>((h_I))</span> denote the standard Haar system on [0, 1], indexed by <span>(Iin mathcal {D})</span>, the set of dyadic intervals and <span>(h_Iotimes h_J)</span> denote the tensor product <span>((s,t)mapsto h_I(s) h_J(t))</span>, <span>(I,Jin mathcal {D})</span>. We consider a class of two-parameter function spaces which are completions of the linear span <span>(mathcal {V}(delta ^2))</span> of <span>(h_Iotimes h_J)</span>, <span>(I,Jin mathcal {D})</span>. This class contains all the spaces of the form <i>X</i>(<i>Y</i>), where <i>X</i> and <i>Y</i> are either the Lebesgue spaces <span>(L^p[0,1])</span> or the Hardy spaces <span>(H^p[0,1])</span>, <span>(1le p &lt; infty )</span>. We say that <span>(D:X(Y)rightarrow X(Y))</span> is a Haar multiplier if <span>(D(h_Iotimes h_J) = d_{I,J} h_Iotimes h_J)</span>, where <span>(d_{I,J}in mathbb {R})</span>, and ask which more elementary operators factor through <i>D</i>. A decisive role is played by the <i>Capon projection</i> <span>(mathcal {C}:mathcal {V}(delta ^2)rightarrow mathcal {V}(delta ^2))</span> given by <span>(mathcal {C} h_Iotimes h_J = h_Iotimes h_J)</span> if <span>(|I|le |J|)</span>, and <span>(mathcal {C} h_Iotimes h_J = 0)</span> if <span>(|I| &gt; |J|)</span>, as our main result highlights: Given any bounded Haar multiplier <span>(D:X(Y)rightarrow X(Y))</span>, there exist <span>(lambda ,mu in mathbb {R})</span> such that </p><span>$$begin{aligned} lambda mathcal {C} + mu ({{,textrm{Id},}}-mathcal {C})text { approximately 1-projectionally factors through }D, end{aligned}$$</span><p>i.e., for all <span>(eta &gt; 0)</span>, there exist bounded operators <i>A</i>, <i>B</i> so that <i>AB</i> is the identity operator <span>({{,textrm{Id},}})</span>, <span>(Vert AVert cdot Vert BVert = 1)</span> and <span>(Vert lambda mathcal {C} + mu ({{,textrm{Id},}}-mathcal {C}) - ADBVert &lt; eta )</span>. Additionally, if <span>(mathcal {C})</span> is unbounded on <i>X</i>(<i>Y</i>), then <span>(lambda = mu )</span> and then <span>({{,textrm{Id},}})</span> either factors through <i>D</i> or <span>({{,textrm{Id},}}-D)</span>.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"68 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141148981","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":"Higher Hölder regularity for the fractional p-Laplace equation in the subquadratic case","authors":"Prashanta Garain, Erik Lindgren","doi":"10.1007/s00208-024-02891-z","DOIUrl":"https://doi.org/10.1007/s00208-024-02891-z","url":null,"abstract":"<p>We study the fractional <i>p</i>-Laplace equation </p><span>$$begin{aligned} (-Delta _p)^s u = 0 end{aligned}$$</span><p>for <span>(0&lt;s&lt;1)</span> and in the subquadratic case <span>(1&lt;p&lt;2)</span>. We provide Hölder estimates with an explicit Hölder exponent. The inhomogeneous equation is also treated and there the exponent obtained is almost sharp for a certain range of parameters. Our results complement the previous results for the superquadratic case when <span>(pge 2)</span>. The arguments are based on a careful Moser-type iteration and a perturbation argument.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"45 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141148980","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}