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On Gaussian decay rates of harmonic oscillators and equivalences of related Fourier uncertainty principles 谐波振子的高斯衰减率及相关傅立叶测不准原理的等价
IF 1.2 2区 数学
Revista Matematica Iberoamericana Pub Date : 2022-02-22 DOI: 10.4171/rmi/1426
A. Kulikov, Lucas H. Oliveira, João P. G. Ramos
{"title":"On Gaussian decay rates of harmonic oscillators and equivalences of related Fourier uncertainty principles","authors":"A. Kulikov, Lucas H. Oliveira, João P. G. Ramos","doi":"10.4171/rmi/1426","DOIUrl":"https://doi.org/10.4171/rmi/1426","url":null,"abstract":"We make progress on a question by Vemuri on the optimal Gaussian decay of harmonic oscillators, proving the original conjecture up to an arithmetic progression of times. The techniques used are a suitable translation of the problem at hand in terms of the free Schr\"odinger equation, the machinery developed in the work of Cowling, Escauriaza, Kenig, Ponce and Vega , and a lemma which relates decay on average to pointwise decay. Such a lemma produces many more consequences in terms of equivalences of uncertainty principles. Complementing such results, we provide endpoint results in particular classes induced by certain Laplace transforms, both to the decay Lemma and to the remaining cases of Vemuri's conjecture, shedding light on the full endpoint question.","PeriodicalId":49604,"journal":{"name":"Revista Matematica Iberoamericana","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2022-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41684696","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: 3
The Calabi–Yau problem for minimal surfaces with Cantor ends 具有Cantor端的极小曲面的Calabi–Yau问题
IF 1.2 2区 数学
Revista Matematica Iberoamericana Pub Date : 2022-02-15 DOI: 10.4171/rmi/1365
F. Forstnerič
{"title":"The Calabi–Yau problem for minimal surfaces with Cantor ends","authors":"F. Forstnerič","doi":"10.4171/rmi/1365","DOIUrl":"https://doi.org/10.4171/rmi/1365","url":null,"abstract":"A BSTRACT . We show that every connected compact or bordered Riemann surface contains a Cantor set whose complement admits a complete conformal minimal immersion in R 3 with bounded image. The analogous result holds for holomorphic immersions into any complex manifold of dimension at least 2 , for holomorphic null immersions into C n with n ≥ 3 , for holomorphic Legendrian immersions into an arbitrary complex contact manifold, and for superminimal immersions into any self-dual or anti-self-dual Einstein four-manifold.","PeriodicalId":49604,"journal":{"name":"Revista Matematica Iberoamericana","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2022-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47494438","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: 2
Paraproducts, Bloom BMO and sparse BMO functions 副积、Bloom BMO和稀疏BMO函数
IF 1.2 2区 数学
Revista Matematica Iberoamericana Pub Date : 2022-01-17 DOI: 10.4171/rmi/1400
Valentia Fragkiadaki, Irina Holmes Fay
{"title":"Paraproducts, Bloom BMO and sparse BMO functions","authors":"Valentia Fragkiadaki, Irina Holmes Fay","doi":"10.4171/rmi/1400","DOIUrl":"https://doi.org/10.4171/rmi/1400","url":null,"abstract":"A. We address Lp(μ) → Lp(λ) bounds for paraproducts in the Bloom setting. We introduce certain “sparse BMO” functions associated with sparse collections with no infinitely increasing chains, and use these to express sparse operators as sums of paraproducts and martingale transforms – essentially, as Haar multipliers – as well as to obtain an equivalence of norms between sparse operators AS and compositions of paraproducts ΠaΠb.","PeriodicalId":49604,"journal":{"name":"Revista Matematica Iberoamericana","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2022-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48806029","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: 1
Non-locality, non-linearity, and existence of solutions to the Dirichlet problem for least gradient functions in metric measure spaces 度量测度空间中最小梯度函数Dirichlet问题解的非局部性、非线性和存在性
IF 1.2 2区 数学
Revista Matematica Iberoamericana Pub Date : 2022-01-08 DOI: 10.4171/rmi/1385
Joshua Kline
{"title":"Non-locality, non-linearity, and existence of solutions to the Dirichlet problem for least gradient functions in metric measure spaces","authors":"Joshua Kline","doi":"10.4171/rmi/1385","DOIUrl":"https://doi.org/10.4171/rmi/1385","url":null,"abstract":"We study the Dirichlet problem for least gradient functions for domains in metric spaces equipped with a doubling measure and supporting a (1,1)-Poincaré inequality when the boundary of the domain satisfies a positive mean curvature condition. In this setting, it was shown by Malý, Lahti, Shanmugalingam, and Speight that solutions exist for continuous boundary data. We extend these results, showing existence of solutions for boundary data that is approximable from above and below by continuous functions. We also show that for each f ∈ L 1 ( ∂ Ω) , there is a least gradient function in Ω whose trace agrees with f at points of continuity of f , and so we obtain existence of solutions for boundary data which is continuous almost everywhere. This is in contrast to a result of Spradlin and Tamasan, who constructed an L 1 -function on the unit circle which has no least gradient solution in the unit disk in R 2 . Modifying the example of Spradlin and Tamasan, we show that the space of solvable L 1 -functions on the unit circle is non-linear, even though the unit disk satisfies the positive mean curvature condition.","PeriodicalId":49604,"journal":{"name":"Revista Matematica Iberoamericana","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2022-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44138346","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: 2
Minimal Mahler measures for generators of some fields 某些域的生成元的极小Mahler测度
IF 1.2 2区 数学
Revista Matematica Iberoamericana Pub Date : 2022-01-03 DOI: 10.4171/rmi/1331
A. Dubickas
{"title":"Minimal Mahler measures for generators of some fields","authors":"A. Dubickas","doi":"10.4171/rmi/1331","DOIUrl":"https://doi.org/10.4171/rmi/1331","url":null,"abstract":"","PeriodicalId":49604,"journal":{"name":"Revista Matematica Iberoamericana","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2022-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44997767","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: 1
How highly connected can an orbifold be? 一个轨道的连接能有多高?
IF 1.2 2区 数学
Revista Matematica Iberoamericana Pub Date : 2021-12-29 DOI: 10.4171/rmi/1375
Christian Lange, M. Radeschi
{"title":"How highly connected can an orbifold be?","authors":"Christian Lange, M. Radeschi","doi":"10.4171/rmi/1375","DOIUrl":"https://doi.org/10.4171/rmi/1375","url":null,"abstract":"On the one hand, we provide the first examples of arbitrarily highly connected (compact) bad orbifolds. On the other hand, we show that n-connected norbifolds are manifolds. The latter improves the best previously known bound of Lytchak by roughly a factor of 2. For compact orbifolds and in most dimensions we prove slightly better bounds. We obtain sharp results up to dimension 5.","PeriodicalId":49604,"journal":{"name":"Revista Matematica Iberoamericana","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2021-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41814838","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: 1
Asymptotic $N$-soliton-like solutions of the fractional Korteweg–de Vries equation 分数阶Korteweg-de Vries方程的渐近类N孤子解
IF 1.2 2区 数学
Revista Matematica Iberoamericana Pub Date : 2021-12-21 DOI: 10.4171/rmi/1396
Arnaud Eychenne
{"title":"Asymptotic $N$-soliton-like solutions of the fractional Korteweg–de Vries equation","authors":"Arnaud Eychenne","doi":"10.4171/rmi/1396","DOIUrl":"https://doi.org/10.4171/rmi/1396","url":null,"abstract":"We construct $N$-soliton solutions for the fractional Korteweg-de Vries (fKdV) equation $$ partial_t u - partial_xleft(|D|^{alpha}u - u^2 right)=0, $$ in the whole sub-critical range $alpha in]frac12,2[$. More precisely, if $Q_c$ denotes the ground state solution associated to fKdV evolving with velocity $c$, then given $0<c_1<cdots<c_N$, we prove the existence of a solution $U$ of (fKdV) satisfying $$ lim_{ttoinfty} | U(t,cdot) - sum_{j=1}^NQ_{c_j}(x-rho_j(t)) |_{H^{frac{alpha}2}}=0, $$ where $rho'_j(t) sim c_j$ as $t to +infty$. The proof adapts the construction of Martel in the generalized KdV setting [Amer. J. Math. 127 (2005), pp. 1103-1140]) to the fractional case. The main new difficulties are the polynomial decay of the ground state $Q_c$ and the use of local techniques (monotonicity properties for a portion of the mass and the energy) for a non-local equation. To bypass these difficulties, we use symmetric and non-symmetric weighted commutator estimates. The symmetric ones were proved by Kenig, Martel and Robbiano [Annales de l'IHP Analyse Non Lin'eaire 28 (2011), pp. 853-887], while the non-symmetric ones seem to be new.","PeriodicalId":49604,"journal":{"name":"Revista Matematica Iberoamericana","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2021-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46861832","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: 3
A non-local inverse problem with boundary response 一个具有边界响应的非局部逆问题
IF 1.2 2区 数学
Revista Matematica Iberoamericana Pub Date : 2021-12-15 DOI: 10.4171/rmi/1323
T. Ghosh
{"title":"A non-local inverse problem with boundary response","authors":"T. Ghosh","doi":"10.4171/rmi/1323","DOIUrl":"https://doi.org/10.4171/rmi/1323","url":null,"abstract":"","PeriodicalId":49604,"journal":{"name":"Revista Matematica Iberoamericana","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2021-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44535467","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: 7
Distribution symmetry of toral eigenfunctions 所有特征函数的分布对称性
IF 1.2 2区 数学
Revista Matematica Iberoamericana Pub Date : 2021-12-13 DOI: 10.4171/rmi/1324
'Angel D. Mart'inez, Francisco Torres de Lizaur
{"title":"Distribution symmetry of toral eigenfunctions","authors":"'Angel D. Mart'inez, Francisco Torres de Lizaur","doi":"10.4171/rmi/1324","DOIUrl":"https://doi.org/10.4171/rmi/1324","url":null,"abstract":". In this paper we study a number of conjectures on the behavior of the value distribution of eigenfunctions. On the two dimensional torus we observe that the symmetry conjecture holds in the strongest possible sense. On the other hand we provide a counterexample for higher dimensional tori, which relies on a computer assisted argument. Moreover we prove a theorem on the distribution symmetry of a certain class of trigonometric polynomials that might be of independent interest. eigenfuntions on Riemannian manifolds.","PeriodicalId":49604,"journal":{"name":"Revista Matematica Iberoamericana","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2021-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48137908","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: 3
Closed $G_2$-eigenforms and exact $G_2$-structures 闭$G_2$-本征形式与精确$G_2$结构
IF 1.2 2区 数学
Revista Matematica Iberoamericana Pub Date : 2021-12-03 DOI: 10.4171/rmi/1315
Marco Freibert, S. Salamon
{"title":"Closed $G_2$-eigenforms and exact $G_2$-structures","authors":"Marco Freibert, S. Salamon","doi":"10.4171/rmi/1315","DOIUrl":"https://doi.org/10.4171/rmi/1315","url":null,"abstract":"","PeriodicalId":49604,"journal":{"name":"Revista Matematica Iberoamericana","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2021-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49020839","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: 2
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