Pub Date : 2026-01-06DOI: 10.1016/j.jfa.2025.111332
Matías Díaz-Vera , Carlos Román
We consider extreme type-II superconductors modeled by the Ginzburg–Landau energy with a pinning term , which we assume to be a bounded measurable function such that for some constant . A crucial feature of this type of superconductors is the occurrence of vortices, which appear above the so-called first critical field . In this paper we estimate this value and characterize the behavior of the Meissner solution, the unique vortexless configuration that globally minimizes the energy below . In addition, we show that beyond this value, for applied fields whose strength is slightly below the so-called superheating field , there exists a unique Meissner-type solution that locally minimizes the energy.
{"title":"On the Meissner state for type-II inhomogeneous superconductors","authors":"Matías Díaz-Vera , Carlos Román","doi":"10.1016/j.jfa.2025.111332","DOIUrl":"10.1016/j.jfa.2025.111332","url":null,"abstract":"<div><div>We consider extreme type-II superconductors modeled by the Ginzburg–Landau energy with a pinning term <span><math><msub><mrow><mi>a</mi></mrow><mrow><mi>ε</mi></mrow></msub><mo>(</mo><mi>x</mi><mo>)</mo></math></span>, which we assume to be a bounded measurable function such that <span><math><mi>b</mi><mo>≤</mo><msub><mrow><mi>a</mi></mrow><mrow><mi>ε</mi></mrow></msub><mo>(</mo><mi>x</mi><mo>)</mo><mo>≤</mo><mn>1</mn></math></span> for some constant <span><math><mi>b</mi><mo>></mo><mn>0</mn></math></span>. A crucial feature of this type of superconductors is the occurrence of vortices, which appear above the so-called first critical field <span><math><msub><mrow><mi>H</mi></mrow><mrow><msub><mrow><mi>c</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></msub></math></span>. In this paper we estimate this value and characterize the behavior of the Meissner solution, the unique vortexless configuration that globally minimizes the energy below <span><math><msub><mrow><mi>H</mi></mrow><mrow><msub><mrow><mi>c</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></msub></math></span>. In addition, we show that beyond this value, for applied fields whose strength is slightly below the so-called superheating field <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>s</mi><mi>h</mi></mrow></msub></math></span>, there exists a unique Meissner-type solution that locally minimizes the energy.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 7","pages":"Article 111332"},"PeriodicalIF":1.6,"publicationDate":"2026-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145922957","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}
Pub Date : 2026-01-05DOI: 10.1016/j.jfa.2025.111336
Xilun Li, Yanan Ye
In this note, we construct a series of examples to show that various nonnegative curvature conditions, including Riemannian curvature and Bismut curvature, are not preserved by the generalized Ricci flow.
{"title":"Nonnegativity of curvature along generalized Ricci flow","authors":"Xilun Li, Yanan Ye","doi":"10.1016/j.jfa.2025.111336","DOIUrl":"10.1016/j.jfa.2025.111336","url":null,"abstract":"<div><div>In this note, we construct a series of examples to show that various nonnegative curvature conditions, including Riemannian curvature and Bismut curvature, are not preserved by the generalized Ricci flow.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 7","pages":"Article 111336"},"PeriodicalIF":1.6,"publicationDate":"2026-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145922958","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}
Pub Date : 2026-01-05DOI: 10.1016/j.jfa.2025.111334
Miriam Gordin
We present vector-valued concentration inequalities for the biased measure on the discrete cube with an optimal dependence on the bias parameter and the Rademacher type of the target Banach space. These results allow us to obtain novel vector-valued concentration inequalities for the measure given by a product of Poisson distributions. We further obtain lower bounds on the average distortion with respect to the biased measure of embeddings of the hypercube into Banach spaces of nontrivial type which imply average non-embeddability.
{"title":"Vector-valued concentration inequalities on the biased discrete cube","authors":"Miriam Gordin","doi":"10.1016/j.jfa.2025.111334","DOIUrl":"10.1016/j.jfa.2025.111334","url":null,"abstract":"<div><div>We present vector-valued concentration inequalities for the biased measure on the discrete cube <span><math><msup><mrow><mo>{</mo><mo>−</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></mrow><mrow><mi>n</mi></mrow></msup></math></span> with an optimal dependence on the bias parameter and the Rademacher type of the target Banach space. These results allow us to obtain novel vector-valued concentration inequalities for the measure given by a product of Poisson distributions. We further obtain lower bounds on the average distortion with respect to the biased measure of embeddings of the hypercube into Banach spaces of nontrivial type which imply average non-embeddability.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 7","pages":"Article 111334"},"PeriodicalIF":1.6,"publicationDate":"2026-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145922959","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}
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