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Curvature, Diameter and Signs of Graphs 图形的曲率、直径和符号
The Journal of Geometric Analysis Pub Date : 2024-08-31 DOI: 10.1007/s12220-024-01774-8
Wei Chen, Shiping Liu
{"title":"Curvature, Diameter and Signs of Graphs","authors":"Wei Chen, Shiping Liu","doi":"10.1007/s12220-024-01774-8","DOIUrl":"https://doi.org/10.1007/s12220-024-01774-8","url":null,"abstract":"<p>We prove a Li-Yau type eigenvalue-diameter estimate for signed graphs. That is, the nonzero eigenvalues of the Laplacian of a non-negatively curved signed graph are lower bounded by <span>(1/D^2)</span> up to a constant, where <i>D</i> stands for the diameter. This leads to several interesting applications, including a volume estimate for non-negatively curved signed graphs in terms of frustration index and diameter, and a two-sided Li-Yau estimate for triangle-free graphs. Our proof is built upon a combination of Chung-Lin-Yau type gradient estimate and a new trick involving strong nodal domain walks of signed graphs. We further discuss extensions of part of our results to nonlinear Laplacians on signed graphs.</p>","PeriodicalId":501200,"journal":{"name":"The Journal of Geometric Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142190131","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
New Expanding Ricci Solitons Starting in Dimension Four 始于四维的新扩展里奇孤子
The Journal of Geometric Analysis Pub Date : 2024-08-31 DOI: 10.1007/s12220-024-01778-4
Jan Nienhaus, Matthias Wink
{"title":"New Expanding Ricci Solitons Starting in Dimension Four","authors":"Jan Nienhaus, Matthias Wink","doi":"10.1007/s12220-024-01778-4","DOIUrl":"https://doi.org/10.1007/s12220-024-01778-4","url":null,"abstract":"<p>We prove that there exists a gradient expanding Ricci soliton asymptotic to any given cone over the product of a round sphere and a Ricci flat manifold. In particular we obtain asymptotically conical expanding Ricci solitons with positive scalar curvature on <span>(mathbb {R}^3 times S^1.)</span> More generally we construct continuous families of gradient expanding Ricci solitons on trivial vector bundles over products of Einstein manifolds with arbitrary Einstein constants.</p>","PeriodicalId":501200,"journal":{"name":"The Journal of Geometric Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142190133","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On Finite Parts of Divergent Complex Geometric Integrals and Their Dependence on a Choice of Hermitian Metric 论发散复几何积分的有限部分及其与赫米蒂公设选择的关系
The Journal of Geometric Analysis Pub Date : 2024-08-29 DOI: 10.1007/s12220-024-01773-9
Ludvig Svensson
{"title":"On Finite Parts of Divergent Complex Geometric Integrals and Their Dependence on a Choice of Hermitian Metric","authors":"Ludvig Svensson","doi":"10.1007/s12220-024-01773-9","DOIUrl":"https://doi.org/10.1007/s12220-024-01773-9","url":null,"abstract":"<p>Let <i>X</i> be a reduced complex space of pure dimension. We consider divergent integrals of certain forms on <i>X</i> that are singular along a subvariety defined by the zero set of a holomorphic section of some holomorphic vector bundle <span>(E rightarrow X)</span>. Given a choice of Hermitian metric on <i>E</i> we define a finite part of the divergent integral. Our main result is an explicit formula for the dependence on the choice of metric of the finite part.\u0000</p>","PeriodicalId":501200,"journal":{"name":"The Journal of Geometric Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142190134","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Unramified Riemann Domains Satisfying the Oka–Grauert Principle over a Stein Manifold 满足 Stein Manifold 上奥卡-格劳尔特原理的非ramified 黎曼域
The Journal of Geometric Analysis Pub Date : 2024-08-27 DOI: 10.1007/s12220-024-01756-w
Makoto Abe, Shun Sugiyama
{"title":"Unramified Riemann Domains Satisfying the Oka–Grauert Principle over a Stein Manifold","authors":"Makoto Abe, Shun Sugiyama","doi":"10.1007/s12220-024-01756-w","DOIUrl":"https://doi.org/10.1007/s12220-024-01756-w","url":null,"abstract":"<p>Let <span>((D, pi ))</span> be an unramified Riemann domain over a Stein manifold of dimension <i>n</i>. Assume that <span>(H^k(D,mathscr {O}) = 0)</span> for <span>(2 le k le n - 1)</span> and there exists a complex Lie group <i>G</i> of positive dimension such that all differentiably trivial holomorphic principal <i>G</i>-bundles on <i>D</i> are holomorphically trivial. Then, we prove that <i>D</i> is Stein.</p>","PeriodicalId":501200,"journal":{"name":"The Journal of Geometric Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142190135","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Proof that a Form of Rubio de Francia’s Conjectured Littlewood-Paley Type Inequality for $$A_{1}left( {mathbb {R}}right) $$ -Weighted $$L^{2}left( {mathbb {R}}right) $$ is Valid for Every Even $$A_{1}left( {mathbb {R}}right) $$ Weight 证明鲁比奥-德-弗朗西亚猜想的利特尔伍德-佩利式不等式中的 $$A_{1}left( {mathbb {R}right) $$ -加权 $$L^{2}left( {mathbb {R}right) $$ 对于每个偶数 $$A_{1}left( {mathbb {R}right) $$ 加权都是有效的
The Journal of Geometric Analysis Pub Date : 2024-08-24 DOI: 10.1007/s12220-024-01762-y
Earl Berkson
{"title":"Proof that a Form of Rubio de Francia’s Conjectured Littlewood-Paley Type Inequality for $$A_{1}left( {mathbb {R}}right) $$ -Weighted $$L^{2}left( {mathbb {R}}right) $$ is Valid for Every Even $$A_{1}left( {mathbb {R}}right) $$ Weight","authors":"Earl Berkson","doi":"10.1007/s12220-024-01762-y","DOIUrl":"https://doi.org/10.1007/s12220-024-01762-y","url":null,"abstract":"<p>It is demonstrated that a form of Rubio de Francia’s hitherto unresolved Littlewood-Paley Type Conjecture from the year 1985 is valid for the weighted-<span>(L^{2}left( {mathbb {R}}right) )</span> space corresponding to any even <span>(A_{1}left( {mathbb {R}}right) )</span> weight. Otherwise expressed, we show that if <span>(omega )</span> is any even <span>(A_{1}left( {mathbb {R}}right) )</span> weight, <i>C</i> is an <span>(A_{1}left( {mathbb {R}}right) )</span> weight constant for <span>(omega )</span>, <span>( fin )</span> <span>(L^{2}left( {mathbb {R}},omega left( tright) dtright) )</span>, and <span>(left{ J_{k}right} _{kge 1})</span> is any finite or infinite sequence of disjoint intervals of <span>({mathbb {R}})</span>, then the following estimate holds for the corresponding Littlewood-Paley Type square function defined by <span>(left{ S_{J_{k}}left( fright) right} _{kge 1})</span>(where the symbol <span>(S_{_{J_{k}} })</span> denotes the indicated partial sum projection for the context of <span>({mathbb {R}})</span>): </p><span>$$begin{aligned} left| left{ sum limits _{kge 1}left| S_{J_{k}}left( fright) right| ^{2}right} ^{1/2}right| _{L^{2}left( {mathbb {R}},omega left( tright) dtright) }le 2^{5}C^{1/2}left| fright| _{L^{2}left( {mathbb {R}},omega ^*left( tright) dtright) }, end{aligned}$$</span><p>where <span>(omega ^*)</span> is the decreasing rearrangement of <span>(omega )</span>. A corollary of this even <span>(A_{1}left( {mathbb {R}}right) )</span>-weighted theorem is obtained which provides a related variant thereof in the setting of any (not necessarily even) <span>(A_{1}left( {mathbb {R}}right) )</span> weight.</p>","PeriodicalId":501200,"journal":{"name":"The Journal of Geometric Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142224863","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Normalized Solutions to at Least Mass Critical Problems: Singular Polyharmonic Equations and Related Curl–Curl Problems 至少质量临界问题的归一化解：奇异多谐方程及相关的曲线-曲线问题
The Journal of Geometric Analysis Pub Date : 2024-08-23 DOI: 10.1007/s12220-024-01770-y
Bartosz Bieganowski, Jarosław Mederski, Jacopo Schino
{"title":"Normalized Solutions to at Least Mass Critical Problems: Singular Polyharmonic Equations and Related Curl–Curl Problems","authors":"Bartosz Bieganowski, Jarosław Mederski, Jacopo Schino","doi":"10.1007/s12220-024-01770-y","DOIUrl":"https://doi.org/10.1007/s12220-024-01770-y","url":null,"abstract":"<p>We are interested in the existence of normalized solutions to the problem </p><span>$$begin{aligned} {left{ begin{array}{ll} (-Delta )^m u+frac{mu }{|y|^{2m}}u + lambda u = g(u), quad x = (y,z) in mathbb {R}^K times mathbb {R}^{N-K}, int _{mathbb {R}^N} |u|^2 , dx = rho &gt; 0, end{array}right. } end{aligned}$$</span><p>in the so-called at least mass critical regime. We utilize recently introduced variational techniques involving the minimization on the <span>(L^2)</span>-ball. Moreover, we find also a solution to the related curl–curl problem </p><span>$$begin{aligned} {left{ begin{array}{ll} nabla times nabla times textbf{U}+lambda textbf{U}=f(textbf{U}), quad x in mathbb {R}^N, int _{mathbb {R}^N}|textbf{U}|^2,dx=rho , end{array}right. } end{aligned}$$</span><p>which arises from the system of Maxwell equations and is of great importance in nonlinear optics.</p>","PeriodicalId":501200,"journal":{"name":"The Journal of Geometric Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142190136","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On Polynomial Carleson Operators Along Quadratic Hypersurfaces 论沿二次超曲面的多项式卡莱森算子
The Journal of Geometric Analysis Pub Date : 2024-08-23 DOI: 10.1007/s12220-024-01676-9
Theresa C. Anderson, Dominique Maldague, Lillian B. Pierce, Po-Lam Yung
{"title":"On Polynomial Carleson Operators Along Quadratic Hypersurfaces","authors":"Theresa C. Anderson, Dominique Maldague, Lillian B. Pierce, Po-Lam Yung","doi":"10.1007/s12220-024-01676-9","DOIUrl":"https://doi.org/10.1007/s12220-024-01676-9","url":null,"abstract":"<p>We prove that a maximally modulated singular oscillatory integral operator along a hypersurface defined by <span>((y,Q(y))subseteq mathbb {R}^{n+1})</span>, for an arbitrary non-degenerate quadratic form <i>Q</i>, admits an <i>a priori</i> bound on <span>(L^p)</span> for all <span>(1&lt;p&lt;infty )</span>, for each <span>(n ge 2)</span>. This operator takes the form of a polynomial Carleson operator of Radon-type, in which the maximally modulated phases lie in the real span of <span>({p_2,ldots ,p_d})</span> for any set of fixed real-valued polynomials <span>(p_j)</span> such that <span>(p_j)</span> is homogeneous of degree <i>j</i>, and <span>(p_2)</span> is not a multiple of <i>Q</i>(<i>y</i>). The general method developed in this work applies to quadratic forms of arbitrary signature, while previous work considered only the special positive definite case <span>(Q(y)=|y|^2)</span>.</p>","PeriodicalId":501200,"journal":{"name":"The Journal of Geometric Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142190137","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Degenerate Complex Monge–Ampère Equations on Some Compact Hermitian Manifolds 一些紧凑赫尔墨斯漫场上的退化复蒙哥-安培方程
The Journal of Geometric Analysis Pub Date : 2024-08-21 DOI: 10.1007/s12220-024-01772-w
Omar Alehyane, Chinh H. Lu, Mohammed Salouf
{"title":"Degenerate Complex Monge–Ampère Equations on Some Compact Hermitian Manifolds","authors":"Omar Alehyane, Chinh H. Lu, Mohammed Salouf","doi":"10.1007/s12220-024-01772-w","DOIUrl":"https://doi.org/10.1007/s12220-024-01772-w","url":null,"abstract":"<p>Let <i>X</i> be a compact complex manifold which admits a hermitian metric satisfying a curvature condition introduced by Guan–Li. Given a semipositive form <span>(theta )</span> with positive volume, we define the Monge–Ampère operator for unbounded <span>(theta )</span>-psh functions and prove that it is continuous with respect to convergence in capacity. We then develop pluripotential tools to study degenerate complex Monge–Ampère equations in this context, extending recent results of Tosatti–Weinkove, Kolodziej–Nguyen, Guedj–Lu and many others who treat bounded solutions.\u0000</p>","PeriodicalId":501200,"journal":{"name":"The Journal of Geometric Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142190139","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Minimal Networks on Balls and Spheres for Almost Standard Metrics 球和球上几乎标准度量的最小网络
The Journal of Geometric Analysis Pub Date : 2024-08-20 DOI: 10.1007/s12220-024-01765-9
Luciano Sciaraffia
{"title":"Minimal Networks on Balls and Spheres for Almost Standard Metrics","authors":"Luciano Sciaraffia","doi":"10.1007/s12220-024-01765-9","DOIUrl":"https://doi.org/10.1007/s12220-024-01765-9","url":null,"abstract":"<p>We study the existence of minimal networks in the unit sphere <span>({textbf{S}}^d)</span> and the unit ball <span>({textbf{B}}^d)</span> of <span>({textbf{R}}^d)</span> endowed with Riemannian metrics close to the standard ones. We employ a finite-dimensional reduction method, modelled on the configuration of <span>(theta )</span>-networks in <span>({textbf{S}}^d)</span> and triods in <span>({textbf{B}}^d)</span>, jointly with the Lusternik–Schnirelmann category.</p>","PeriodicalId":501200,"journal":{"name":"The Journal of Geometric Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142190146","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
BV Functions and Nonlocal Functionals in Metric Measure Spaces 公度量空间中的 BV 函数和非局部函数
The Journal of Geometric Analysis Pub Date : 2024-08-19 DOI: 10.1007/s12220-024-01766-8
Panu Lahti, Andrea Pinamonti, Xiaodan Zhou
{"title":"BV Functions and Nonlocal Functionals in Metric Measure Spaces","authors":"Panu Lahti, Andrea Pinamonti, Xiaodan Zhou","doi":"10.1007/s12220-024-01766-8","DOIUrl":"https://doi.org/10.1007/s12220-024-01766-8","url":null,"abstract":"<p>We study the asymptotic behavior of three classes of nonlocal functionals in complete metric spaces equipped with a doubling measure and supporting a Poincaré inequality. We show that the limits of these nonlocal functionals are comparable to the total variation <span>(Vert DfVert (Omega ))</span> or the Sobolev semi-norm <span>(int _Omega g_f^p, dmu )</span>, which extends Euclidean results to metric measure spaces. In contrast to the classical setting, we also give an example to show that the limits are not always equal to the corresponding total variation even for Lipschitz functions.</p>","PeriodicalId":501200,"journal":{"name":"The Journal of Geometric Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142190176","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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