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Quantization of the energy for the inhomogeneous Allen–Cahn mean curvature 非均质艾伦-卡恩平均曲率的能量量子化
IF 1.4 2区 数学
Mathematische Annalen Pub Date : 2024-06-14 DOI: 10.1007/s00208-024-02909-6
Huy The Nguyen, Shengwen Wang
{"title":"Quantization of the energy for the inhomogeneous Allen–Cahn mean curvature","authors":"Huy The Nguyen, Shengwen Wang","doi":"10.1007/s00208-024-02909-6","DOIUrl":"https://doi.org/10.1007/s00208-024-02909-6","url":null,"abstract":"<p>We consider the varifold associated to the Allen–Cahn phase transition problem in <span>({mathbb {R}}^{n+1})</span>(or <span>(n+1)</span>-dimensional Riemannian manifolds with bounded curvature) with integral <span>(L^{q_0})</span> bounds on the Allen–Cahn mean curvature (first variation of the Allen–Cahn energy) in this paper. It is shown here that there is an equidistribution of energy between the Dirichlet and Potential energy in the phase field limit and that the associated varifold to the total energy converges to an integer rectifiable varifold with mean curvature in <span>(L^{q_0}, q_0 &gt; n)</span>. The latter is a diffused version of Allard’s convergence theorem for integer rectifiable varifolds.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"113 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141512656","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
Existence of generating families on Lagrangian cobordisms 拉格朗日共线性上族的存在性
IF 1.4 2区 数学
Mathematische Annalen Pub Date : 2024-06-14 DOI: 10.1007/s00208-024-02913-w
Wenyuan Li
{"title":"Existence of generating families on Lagrangian cobordisms","authors":"Wenyuan Li","doi":"10.1007/s00208-024-02913-w","DOIUrl":"https://doi.org/10.1007/s00208-024-02913-w","url":null,"abstract":"<p>For an embedded exact Lagrangian cobordism between Legendrian submanifolds in the 1-jet bundle, we prove that a generating family linear at infinity on the Legendrian at the negative end extends to a generating family linear at infinity on the Lagrangian cobordism after stabilization if and only if the formal obstructions vanish. In particular, a Lagrangian filling with trivial stable Lagrangian Gauss map admits a generating family linear at infinity.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"41 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141512655","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
Bounded Fatou and Julia components of meromorphic functions 有界法图和非定常函数的 Julia 分量
IF 1.4 2区 数学
Mathematische Annalen Pub Date : 2024-06-08 DOI: 10.1007/s00208-023-02725-4
David Martí-Pete, Lasse Rempe, James Waterman
{"title":"Bounded Fatou and Julia components of meromorphic functions","authors":"David Martí-Pete, Lasse Rempe, James Waterman","doi":"10.1007/s00208-023-02725-4","DOIUrl":"https://doi.org/10.1007/s00208-023-02725-4","url":null,"abstract":"<p>We completely characterise the bounded sets that arise as components of the Fatou and Julia sets of meromorphic functions. On the one hand, we prove that a bounded domain is a Fatou component of some meromorphic function if and only if it is regular. On the other hand, we prove that a planar continuum is a Julia component of some meromorphic function if and only if it has empty interior. We do so by constructing meromorphic functions with wandering compacta using approximation theory.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"1 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141548320","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
Bias in the distribution of holonomy on compact hyperbolic 3-manifolds 紧凑双曲3-manifolds上整体性分布的偏差
IF 1.4 2区 数学
Mathematische Annalen Pub Date : 2024-06-06 DOI: 10.1007/s00208-024-02903-y
Lindsay Dever
{"title":"Bias in the distribution of holonomy on compact hyperbolic 3-manifolds","authors":"Lindsay Dever","doi":"10.1007/s00208-024-02903-y","DOIUrl":"https://doi.org/10.1007/s00208-024-02903-y","url":null,"abstract":"<p>Ambient prime geodesic theorems provide an asymptotic count of closed geodesics by their length and holonomy and imply effective equidistribution of holonomy. We show that for a smoothed count of closed geodesics on compact hyperbolic 3-manifolds, there is a persistent bias in the secondary term which is controlled by the number of zero spectral parameters. In addition, we show that a normalized, smoothed bias count is distributed according to a probability distribution, which we explicate when all distinct, non-zero spectral parameters are linearly independent.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"27 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141512657","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
Fractional Sobolev spaces on Riemannian manifolds 黎曼流形上的分数索波列夫空间
IF 1.4 2区 数学
Mathematische Annalen Pub Date : 2024-06-03 DOI: 10.1007/s00208-024-02894-w
Michele Caselli, Enric Florit-Simon, Joaquim Serra
{"title":"Fractional Sobolev spaces on Riemannian manifolds","authors":"Michele Caselli, Enric Florit-Simon, Joaquim Serra","doi":"10.1007/s00208-024-02894-w","DOIUrl":"https://doi.org/10.1007/s00208-024-02894-w","url":null,"abstract":"<p>This article studies the canonical Hilbert energy <span>(H^{s/2}(M))</span> on a Riemannian manifold for <span>(sin (0,2))</span>, with particular focus on the case of closed manifolds. Several equivalent definitions for this energy and the fractional Laplacian on a manifold are given, and they are shown to be identical up to explicit multiplicative constants. Moreover, the precise behavior of the kernel associated with the singular integral definition of the fractional Laplacian is obtained through an in-depth study of the heat kernel on a Riemannian manifold. Furthermore, a monotonicity formula for stationary points of functionals of the type <span>({mathcal {E}}(v)=[v]^2_{H^{s/2}(M)}+int _M F(v) , dV)</span>, with <span>(Fge 0)</span>, is given, which includes in particular the case of nonlocal <i>s</i>-minimal surfaces. Finally, we prove some estimates for the Caffarelli–Silvestre extension problem, which are of general interest. This work is motivated by Caselli et al. (Yau’s conjecture for nonlocal minimal surfaces, arxiv preprint, 2023), which defines nonlocal minimal surfaces on closed Riemannian manifolds and shows the existence of infinitely many of them for any metric on the manifold, ultimately proving the nonlocal version of a conjecture of Yau (Ann Math Stud 102:669–706, 1982). Indeed, the definitions and results in the present work serve as an essential technical toolbox for the results in Caselli et al. (Yau’s conjecture for nonlocal minimal surfaces, arxiv preprint, 2023).</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"35 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141259069","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
Generalized Schauder theory and its application to degenerate/singular parabolic equations 广义绍德理论及其在退化/星状抛物方程中的应用
IF 1.4 2区 数学
Mathematische Annalen Pub Date : 2024-06-03 DOI: 10.1007/s00208-024-02898-6
Takwon Kim, Ki-Ahm Lee, Hyungsung Yun
{"title":"Generalized Schauder theory and its application to degenerate/singular parabolic equations","authors":"Takwon Kim, Ki-Ahm Lee, Hyungsung Yun","doi":"10.1007/s00208-024-02898-6","DOIUrl":"https://doi.org/10.1007/s00208-024-02898-6","url":null,"abstract":"<p>In this paper, we study generalized Schauder theory for the degenerate/singular parabolic equations of the form </p><span>$$begin{aligned} u_t = a^{i'j'}u_{i'j'} + 2 x_n^{gamma /2} a^{i'n} u_{i'n} + x_n^{gamma } a^{nn} u_{nn} + b^{i'} u_{i'} + x_n^{gamma /2} b^n u_{n} + c u + f quad (gamma le 1). end{aligned}$$</span><p>When the equation above is singular, it can be derived from Monge–Ampère equations by using the partial Legendre transform. Also, we study the fractional version of Taylor expansion for the solution <i>u</i>, which is called <i>s</i>-polynomial. To prove <span>(C_s^{2+alpha })</span>-regularity and higher regularity of the solution <i>u</i>, we establish generalized Schauder theory which approximates coefficients of the operator with <i>s</i>-polynomials rather than constants. The generalized Schauder theory not only recovers the proof for uniformly parabolic equations but is also applicable to other operators that are difficult to apply the bootstrap argument to obtain higher regularity.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"53 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141258908","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
Exponential decay for the quintic wave equation with locally distributed damping 具有局部分布阻尼的五次波方程的指数衰减
IF 1.4 2区 数学
Mathematische Annalen Pub Date : 2024-06-03 DOI: 10.1007/s00208-024-02904-x
Marcelo M. Cavalcanti, Valéria N. Domingos Cavalcanti, André Vicente
{"title":"Exponential decay for the quintic wave equation with locally distributed damping","authors":"Marcelo M. Cavalcanti, Valéria N. Domingos Cavalcanti, André Vicente","doi":"10.1007/s00208-024-02904-x","DOIUrl":"https://doi.org/10.1007/s00208-024-02904-x","url":null,"abstract":"<p>We study the stabilization and the well-posedness of solutions of the quintic wave equation with locally distributed damping. The novelty of this paper is that we deal with the difficulty that the main equation does not have good nonlinear structure amenable to a direct proof of a priori bounds and a desirable observability inequality. It is well known that observability inequalities play a critical role in characterizing the long time behaviour of solutions of evolution equations, which is the main goal of this study. In order to address this, we approximate weak solutions for regular solutions for which it is possible to obtain a priori bounds and prove the essential observability inequality. The treatment of these approximate solutions is still a challenging task and requires the use of Strichartz estimates and some microlocal analysis tools such as microlocal defect measures.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"30 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141259060","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
Homology concordance and knot Floer homology 同构协和与结浮子同构
IF 1.4 2区 数学
Mathematische Annalen Pub Date : 2024-06-02 DOI: 10.1007/s00208-024-02906-9
Irving Dai, Jennifer Hom, Matthew Stoffregen, Linh Truong
{"title":"Homology concordance and knot Floer homology","authors":"Irving Dai, Jennifer Hom, Matthew Stoffregen, Linh Truong","doi":"10.1007/s00208-024-02906-9","DOIUrl":"https://doi.org/10.1007/s00208-024-02906-9","url":null,"abstract":"<p>We study the homology concordance group of knots in integer homology three-spheres which bound integer homology four-balls. Using knot Floer homology, we construct an infinite number of <span>(mathbb {Z})</span>-valued, linearly independent homology concordance homomorphisms which vanish for knots coming from <span>(S^3)</span>. This shows that the homology concordance group modulo knots coming from <span>(S^3)</span> contains an infinite-rank summand. The techniques used here generalize the classification program established in previous papers regarding the local equivalence group of knot Floer complexes over <span>(mathbb {F}[U, V]/(UV))</span>. Our results extend this approach to complexes defined over a broader class of rings.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"327 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141192563","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
A sharp Hörmander estimate for multi-parameter and multi-linear Fourier multiplier operators 多参数和多线性傅立叶乘法算子的尖锐霍曼德估计值
IF 1.4 2区 数学
Mathematische Annalen Pub Date : 2024-06-01 DOI: 10.1007/s00208-024-02893-x
Jiao Chen, Danqing He, Guozhen Lu, Bae Jun Park, Lu Zhang
{"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}
引用次数: 0
Trends in Maxillomandibular Fixation Technique at a Single Academic Institution. 一家学术机构的上下颌骨固定技术趋势。
IF 1.3 2区 数学
Mathematische Annalen Pub Date : 2024-06-01 Epub Date: 2023-05-13 DOI: 10.1177/19433875231176339
Heather Schopper, Natalie A Krane, Kevin J Sykes, Katherine Yu, J David Kriet, Clinton D Humphrey
{"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}
引用次数: 0
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