Bulletin of the London Mathematical Society最新文献

{"title":"Lipschitz-free spaces over strongly countable-dimensional spaces and approximation properties","authors":"Filip Talimdjioski","doi":"10.1112/blms.13200","DOIUrl":"https://doi.org/10.1112/blms.13200","url":null,"abstract":"<p>Let <span></span><math>\u0000 <semantics>\u0000 <mi>T</mi>\u0000 <annotation>$T$</annotation>\u0000 </semantics></math> be a compact, metrisable and strongly countable-dimensional topological space. Let <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>M</mi>\u0000 <mi>T</mi>\u0000 </msup>\u0000 <annotation>$mathcal {M}^T$</annotation>\u0000 </semantics></math> be the set of all metrics <span></span><math>\u0000 <semantics>\u0000 <mi>d</mi>\u0000 <annotation>$d$</annotation>\u0000 </semantics></math> on <span></span><math>\u0000 <semantics>\u0000 <mi>T</mi>\u0000 <annotation>$T$</annotation>\u0000 </semantics></math> compatible with its topology, and equip <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>M</mi>\u0000 <mi>T</mi>\u0000 </msup>\u0000 <annotation>$mathcal {M}^T$</annotation>\u0000 </semantics></math> with the topology of uniform convergence, where the metrics are regarded as functions on <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>T</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <annotation>$T^2$</annotation>\u0000 </semantics></math>. We prove that the set <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>A</mi>\u0000 <mrow>\u0000 <mi>T</mi>\u0000 <mo>,</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msup>\u0000 <annotation>$mathcal {A}^{T,1}$</annotation>\u0000 </semantics></math> of metrics <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>d</mi>\u0000 <mo>∈</mo>\u0000 <msup>\u0000 <mi>M</mi>\u0000 <mi>T</mi>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$din mathcal {M}^T$</annotation>\u0000 </semantics></math> for which the Lipschitz-free space <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>F</mi>\u0000 <mo>(</mo>\u0000 <mi>T</mi>\u0000 <mo>,</mo>\u0000 <mi>d</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$mathcal {F}(T,d)$</annotation>\u0000 </semantics></math> has the metric approximation property is residual in <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>M</mi>\u0000 <mi>T</mi>\u0000 </msup>\u0000 <annotation>$mathcal {M}^T$</annotation>\u0000 ","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 2","pages":"359-376"},"PeriodicalIF":0.8,"publicationDate":"2024-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.13200","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143362726","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Continuous actions on primitive ideal spaces lift to \u0000 \u0000 \u0000 C\u0000 *\u0000 \u0000 $mathrm{C}^ast$\u0000 -actions","authors":"Matteo Pagliero","doi":"10.1112/blms.13203","DOIUrl":"https://doi.org/10.1112/blms.13203","url":null,"abstract":"<p>We prove that for any second-countable, locally compact group <span></span><math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math>, any continuous <span></span><math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math>-action on the primitive ideal space of a separable, nuclear <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>C</mi>\u0000 <mo>*</mo>\u0000 </msup>\u0000 <annotation>$mathrm{C}^ast$</annotation>\u0000 </semantics></math>-algebra <span></span><math>\u0000 <semantics>\u0000 <mi>B</mi>\u0000 <annotation>$B$</annotation>\u0000 </semantics></math> such that <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>B</mi>\u0000 <mo>≅</mo>\u0000 <mi>B</mi>\u0000 <mo>⊗</mo>\u0000 <msub>\u0000 <mi>O</mi>\u0000 <mn>2</mn>\u0000 </msub>\u0000 <mo>⊗</mo>\u0000 <mi>K</mi>\u0000 </mrow>\u0000 <annotation>$B cong Botimes mathcal {O}_2otimes mathcal {K}$</annotation>\u0000 </semantics></math> is induced by an action on <span></span><math>\u0000 <semantics>\u0000 <mi>B</mi>\u0000 <annotation>$B$</annotation>\u0000 </semantics></math>. As a direct consequence, we establish that every continuous action on the primitive ideal space of a separable, nuclear <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>C</mi>\u0000 <mo>*</mo>\u0000 </msup>\u0000 <annotation>$mathrm{C}^ast$</annotation>\u0000 </semantics></math>-algebra is induced by an action on a <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>C</mi>\u0000 <mo>*</mo>\u0000 </msup>\u0000 <annotation>$mathrm{C}^ast$</annotation>\u0000 </semantics></math>-algebra with the same primitive ideal space. Moreover, we discuss an application to the classification of equivariantly <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>O</mi>\u0000 <mn>2</mn>\u0000 </msub>\u0000 <annotation>$mathcal {O}_2$</annotation>\u0000 </semantics></math>-stable actions.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 2","pages":"404-425"},"PeriodicalIF":0.8,"publicationDate":"2024-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143362538","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A note on Stein fillability of circle bundles over symplectic manifolds","authors":"Takahiro Oba","doi":"10.1112/blms.13202","DOIUrl":"https://doi.org/10.1112/blms.13202","url":null,"abstract":"<p>We show that, given a closed integral symplectic manifold <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>Σ</mi>\u0000 <mo>,</mo>\u0000 <mi>ω</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(Sigma, omega)$</annotation>\u0000 </semantics></math> of dimension <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 <mi>n</mi>\u0000 <mo>⩾</mo>\u0000 <mn>4</mn>\u0000 </mrow>\u0000 <annotation>$2n geqslant 4$</annotation>\u0000 </semantics></math>, for every integer <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>k</mi>\u0000 <mo>&gt;</mo>\u0000 <msub>\u0000 <mo>∫</mo>\u0000 <mi>Σ</mi>\u0000 </msub>\u0000 <msup>\u0000 <mi>ω</mi>\u0000 <mi>n</mi>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$k&gt;int _{Sigma }omega ^{n}$</annotation>\u0000 </semantics></math>, the Boothby–Wang bundle over <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>Σ</mi>\u0000 <mo>,</mo>\u0000 <mi>k</mi>\u0000 <mi>ω</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(Sigma, komega)$</annotation>\u0000 </semantics></math> carries no Stein fillable contact structure. This negatively answers a question raised by Eliashberg. A similar result holds for Boothby–Wang orbibundles. As an application, we prove the non-smoothability of some isolated singularities.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 2","pages":"395-403"},"PeriodicalIF":0.8,"publicationDate":"2024-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143362396","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A note on ubiquity of geometric Brascamp–Lieb data","authors":"Neal Bez,&nbsp;Anthony Gauvan,&nbsp;Hiroshi Tsuji","doi":"10.1112/blms.13198","DOIUrl":"https://doi.org/10.1112/blms.13198","url":null,"abstract":"<p>Relying substantially on work of Garg, Gurvits, Oliveira and Wigderson, it is shown that geometric Brascamp–Lieb data are, in a certain sense, dense in the space of feasible Brascamp–Lieb data. This addresses a question raised by Bennett and Tao in their recent work on the adjoint Brascamp–Lieb inequality.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 1","pages":"302-314"},"PeriodicalIF":0.8,"publicationDate":"2024-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.13198","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143112395","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Asymptotic behavior of the ground-state solutions of Lane–Emden system","authors":"Yuxia Guo,&nbsp;Yichen Hu,&nbsp;Shaolong Peng,&nbsp;Tingfeng Yuan","doi":"10.1112/blms.13181","DOIUrl":"https://doi.org/10.1112/blms.13181","url":null,"abstract":"<p>In this paper, we consider the following Lane–Emden system:\u0000\u0000 </p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 1","pages":"1-15"},"PeriodicalIF":0.8,"publicationDate":"2024-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.13181","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143110644","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Corrigendum: Deformative magnetic marked length spectrum rigidity","authors":"James Marshall Reber","doi":"10.1112/blms.13195","DOIUrl":"https://doi.org/10.1112/blms.13195","url":null,"abstract":"<p>We describe a mistake in Corollary 3.2 as well as a mistake in Lemma 3.4 of Reber [Bull. London Math. Soc. <b>55</b> (2023), no. 6, 3077–3096], and give an alternative proof of the main result.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"56 12","pages":"3920-3923"},"PeriodicalIF":0.8,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.13195","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142851569","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Piecewise rank-one approximation of vector fields with measure derivatives","authors":"Jean-François Babadjian,&nbsp;Flaviana Iurlano","doi":"10.1112/blms.13190","DOIUrl":"https://doi.org/10.1112/blms.13190","url":null,"abstract":"<p>This work addresses the question of density of piecewise constant (resp. rigid) functions in the space of vector-valued functions with bounded variation (resp. deformation) with respect to the strict convergence. Such an approximation property cannot hold when considering the usual total variation in the space of measures associated to the standard Frobenius norm in the space of matrices. It turns out that oscillation and concentration phenomena interact in such a way that the Frobenius norm has to be homogenized into a (resp. symmetric) Schatten-1 norm that coincides with the Euclidean norm on rank-one (resp. symmetric) matrices. By means of explicit constructions consisting of the superposition of sequential laminates, the validity of an optimal approximation property is established at the expense of endowing the space of measures with a total variation associated with the homogenized norm in the space of matrices.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 1","pages":"181-202"},"PeriodicalIF":0.8,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.13190","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143119458","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Global solutions to semilinear parabolic equations driven by mixed local–nonlocal operators","authors":"Stefano Biagi,&nbsp;Fabio Punzo,&nbsp;Eugenio Vecchi","doi":"10.1112/blms.13196","DOIUrl":"https://doi.org/10.1112/blms.13196","url":null,"abstract":"<p>We are concerned with the Cauchy problem for the semilinear parabolic equation driven by the mixed local–nonlocal operator <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>L</mi>\u0000 <mo>=</mo>\u0000 <mo>−</mo>\u0000 <mi>Δ</mi>\u0000 <mo>+</mo>\u0000 <msup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mo>−</mo>\u0000 <mi>Δ</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mi>s</mi>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$mathcal {L}= -Delta +(-Delta)^s$</annotation>\u0000 </semantics></math>, with a power-like source term. We show that the so-called Fujita phenomenon holds, and the critical value is exactly the same as for the fractional Laplacian.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 1","pages":"265-284"},"PeriodicalIF":0.8,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.13196","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143119547","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Finite subgroups of the profinite completion of good groups","authors":"Marco Boggi,&nbsp;Pavel Zalesskii","doi":"10.1112/blms.13193","DOIUrl":"https://doi.org/10.1112/blms.13193","url":null,"abstract":"<p>Let <span></span><math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math> be a residually finite, good group of finite virtual cohomological dimension. We prove that the natural monomorphism <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 <mo>↪</mo>\u0000 <mover>\u0000 <mi>G</mi>\u0000 <mo>̂</mo>\u0000 </mover>\u0000 </mrow>\u0000 <annotation>$Ghookrightarrow {widehat{G}}$</annotation>\u0000 </semantics></math> induces a bijective correspondence between conjugacy classes of finite <span></span><math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math>-subgroups of <span></span><math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math> and those of its profinite completion <span></span><math>\u0000 <semantics>\u0000 <mover>\u0000 <mi>G</mi>\u0000 <mo>̂</mo>\u0000 </mover>\u0000 <annotation>${widehat{G}}$</annotation>\u0000 </semantics></math>. Moreover, we prove that the centralizers and normalizers in <span></span><math>\u0000 <semantics>\u0000 <mover>\u0000 <mi>G</mi>\u0000 <mo>̂</mo>\u0000 </mover>\u0000 <annotation>${widehat{G}}$</annotation>\u0000 </semantics></math> of finite <span></span><math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math>-subgroups of <span></span><math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math> are the closures of the respective centralizers and normalizers in <span></span><math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math>. With somewhat more restrictive hypotheses, we prove the same results for finite solvable subgroups of <span></span><math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math>. In the last section, we give a few applications of this theorem to hyperelliptic mapping class groups and virtually compact special toral relatively hyperbolic groups (these include fundamental groups of 3-orbifolds and of uniform standard arithmetic hyperbolic orbifolds).</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 1","pages":"236-255"},"PeriodicalIF":0.8,"publicationDate":"2024-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143119159","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On degenerate \u0000 \u0000 \u0000 (\u0000 p\u0000 ,\u0000 q\u0000 )\u0000 \u0000 $(p,q)$\u0000 -Laplace equations corresponding to an inverse spectral problem","authors":"Yavdat Il'yasov,&nbsp;Nur Valeev","doi":"10.1112/blms.13192","DOIUrl":"https://doi.org/10.1112/blms.13192","url":null,"abstract":"<p>A method of solving nonlinear boundary value problems involving <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>p</mi>\u0000 <mo>,</mo>\u0000 <mi>q</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(p,q)$</annotation>\u0000 </semantics></math>-Laplace with unbounded measurable coefficients is introduced through the inverse optimal problem approach. The existence, uniqueness, and stability of the nonnegative weak solution to the nonlinear equations of the form\u0000\u0000 </p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 1","pages":"218-235"},"PeriodicalIF":0.8,"publicationDate":"2024-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143117548","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}