{"title":"Correction to: A monotonicity result for the first Steklov–Dirichlet Laplacian eigenvalue","authors":"Nunzia Gavitone, Gianpaolo Piscitelli","doi":"10.1007/s13163-023-00482-1","DOIUrl":"https://doi.org/10.1007/s13163-023-00482-1","url":null,"abstract":"","PeriodicalId":129004,"journal":{"name":"Revista Matemática Complutense","volume":"85 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138605995","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}
{"title":"Non-negative solutions and strong maximum principle for a resonant quasilinear problem","authors":"Giovanni Anello, Filippo Cammaroto, Luca Vilasi","doi":"10.1007/s13163-023-00481-2","DOIUrl":"https://doi.org/10.1007/s13163-023-00481-2","url":null,"abstract":"","PeriodicalId":129004,"journal":{"name":"Revista Matemática Complutense","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135695720","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}
Bruno Colbois, Alexandre Girouard, Carolyn Gordon, David Sher
{"title":"Some recent developments on the Steklov eigenvalue problem","authors":"Bruno Colbois, Alexandre Girouard, Carolyn Gordon, David Sher","doi":"10.1007/s13163-023-00480-3","DOIUrl":"https://doi.org/10.1007/s13163-023-00480-3","url":null,"abstract":"Abstract The Steklov eigenvalue problem, first introduced over 125 years ago, has seen a surge of interest in the past few decades. This article is a tour of some of the recent developments linking the Steklov eigenvalues and eigenfunctions of compact Riemannian manifolds to the geometry of the manifolds. Topics include isoperimetric-type upper and lower bounds on Steklov eigenvalues (first in the case of surfaces and then in higher dimensions), stability and instability of eigenvalues under deformations of the Riemannian metric, optimisation of eigenvalues and connections to free boundary minimal surfaces in balls, inverse problems and isospectrality, discretisation, and the geometry of eigenfunctions. We begin with background material and motivating examples for readers that are new to the subject. Throughout the tour, we frequently compare and contrast the behavior of the Steklov spectrum with that of the Laplace spectrum. We include many open problems in this rapidly expanding area.","PeriodicalId":129004,"journal":{"name":"Revista Matemática Complutense","volume":"52 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135387149","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}
{"title":"Correction to: The asymptotic Samuel function and invariants of singularities","authors":"A. Benito, A. Bravo, S. Encinas","doi":"10.1007/s13163-023-00475-0","DOIUrl":"https://doi.org/10.1007/s13163-023-00475-0","url":null,"abstract":"","PeriodicalId":129004,"journal":{"name":"Revista Matemática Complutense","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135409851","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}
{"title":"Symmetric finite representability of $$ell ^p$$-spaces in rearrangement invariant spaces on [0, 1]","authors":"Sergey V. Astashkin, Guillermo P. Curbera","doi":"10.1007/s13163-023-00464-3","DOIUrl":"https://doi.org/10.1007/s13163-023-00464-3","url":null,"abstract":"For a separable rearrangement invariant space X on [0, 1] of fundamental type we identify the set of all $$pin [1,infty ]$$ such that $$ell ^p$$ is finitely represented in X in such a way that the unit basis vectors of $$ell ^p$$ ( $$c_0$$ if $$p=infty $$ ) correspond to pairwise disjoint and equimeasurable functions. This can be treated as a follow up of a paper by the first-named author related to separable rearrangement invariant spaces on $$(0,infty )$$ .","PeriodicalId":129004,"journal":{"name":"Revista Matemática Complutense","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135034172","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}