Pub Date : 2022-01-01DOI: 10.4310/cag.2022.v30.n3.a4
Yunlong Zang
{"title":"An integral representation and decay for the wave equation in the extreme Kerr geometry","authors":"Yunlong Zang","doi":"10.4310/cag.2022.v30.n3.a4","DOIUrl":"https://doi.org/10.4310/cag.2022.v30.n3.a4","url":null,"abstract":"","PeriodicalId":50662,"journal":{"name":"Communications in Analysis and Geometry","volume":"1 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70404232","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01DOI: 10.4310/cag.2022.v30.n7.a5
Brian Weber
We study the one-parameter family of twisted Kahler Taub-NUT metrics (discovered by Donaldson), along with two exceptional Taub-NUT-like instantons, and understand them to the extend that should be sufficient for blow-up and gluing arguments. In particular we parametrize their geodesics from the origin, determine curvature fall-off rates, volume growth rates for metric balls, and find blow-down limits.
{"title":"Generalized Kähler Taub-NUT metrics and two exceptional instantons","authors":"Brian Weber","doi":"10.4310/cag.2022.v30.n7.a5","DOIUrl":"https://doi.org/10.4310/cag.2022.v30.n7.a5","url":null,"abstract":"We study the one-parameter family of twisted Kahler Taub-NUT metrics (discovered by Donaldson), along with two exceptional Taub-NUT-like instantons, and understand them to the extend that should be sufficient for blow-up and gluing arguments. In particular we parametrize their geodesics from the origin, determine curvature fall-off rates, volume growth rates for metric balls, and find blow-down limits.","PeriodicalId":50662,"journal":{"name":"Communications in Analysis and Geometry","volume":"1 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70404475","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01DOI: 10.4310/cag.2022.v30.n6.a2
C. R. de Oliveira, A. F. Rossini
{"title":"Effective operators for changing sign Robin Laplacian in thin two- and three-dimensional curved waveguides","authors":"C. R. de Oliveira, A. F. Rossini","doi":"10.4310/cag.2022.v30.n6.a2","DOIUrl":"https://doi.org/10.4310/cag.2022.v30.n6.a2","url":null,"abstract":"","PeriodicalId":50662,"journal":{"name":"Communications in Analysis and Geometry","volume":"1 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70404465","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01DOI: 10.4310/cag.2022.v30.n4.a3
B. Colbois, Ahmad El Soufi, S. Ilias, A. Savo
{"title":"Eigenvalues upper bounds for the magnetic Schrödinger operator","authors":"B. Colbois, Ahmad El Soufi, S. Ilias, A. Savo","doi":"10.4310/cag.2022.v30.n4.a3","DOIUrl":"https://doi.org/10.4310/cag.2022.v30.n4.a3","url":null,"abstract":"","PeriodicalId":50662,"journal":{"name":"Communications in Analysis and Geometry","volume":"1 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70404277","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01DOI: 10.4310/cag.2022.v30.n9.a2
N. Ejiri
We formulate the space of multivalued branched minimal immersions of compact Riemann surfaces of genus γ ≥ 2 into R, and show that it is a complex analytic set. If an irreducible component of the complex analytic set admits a non-degenerate critical point, then we construct a complex Lagrangian cone in H derived from the complex period map, and obtain its applications as follows: The irreducible component can be divided among some open connected components of non-degenerate critical points, and each connected component admits a special pseudo Kähler structure with the signature (p, q). We induce a sharp inequality between q and the Morse index of a minimal surface which are two invariants of the connected component. Furtheremore, we obtain an algorithm to compute the Morse index and the signature.
{"title":"A generating function of a complex Lagrangian cone in $mathbf{H}^n$","authors":"N. Ejiri","doi":"10.4310/cag.2022.v30.n9.a2","DOIUrl":"https://doi.org/10.4310/cag.2022.v30.n9.a2","url":null,"abstract":"We formulate the space of multivalued branched minimal immersions of compact Riemann surfaces of genus γ ≥ 2 into R, and show that it is a complex analytic set. If an irreducible component of the complex analytic set admits a non-degenerate critical point, then we construct a complex Lagrangian cone in H derived from the complex period map, and obtain its applications as follows: The irreducible component can be divided among some open connected components of non-degenerate critical points, and each connected component admits a special pseudo Kähler structure with the signature (p, q). We induce a sharp inequality between q and the Morse index of a minimal surface which are two invariants of the connected component. Furtheremore, we obtain an algorithm to compute the Morse index and the signature.","PeriodicalId":50662,"journal":{"name":"Communications in Analysis and Geometry","volume":"1 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70404667","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01DOI: 10.4310/cag.2022.v30.n2.a6
Qiaoling Xia
{"title":"Local and global gradient estimates for Finsler $p$-harmonic functions","authors":"Qiaoling Xia","doi":"10.4310/cag.2022.v30.n2.a6","DOIUrl":"https://doi.org/10.4310/cag.2022.v30.n2.a6","url":null,"abstract":"","PeriodicalId":50662,"journal":{"name":"Communications in Analysis and Geometry","volume":"1 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70404174","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01DOI: 10.4310/cag.2022.v30.n8.a4
H. D. de Lima, F. R. dos Santos
{"title":"Stochastically complete submanifolds with parallel mean curvature vector field in a Riemannian space form","authors":"H. D. de Lima, F. R. dos Santos","doi":"10.4310/cag.2022.v30.n8.a4","DOIUrl":"https://doi.org/10.4310/cag.2022.v30.n8.a4","url":null,"abstract":"","PeriodicalId":50662,"journal":{"name":"Communications in Analysis and Geometry","volume":"1 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70404536","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01DOI: 10.4310/cag.2022.v30.n9.a5
Chi-Cheung Poon
{"title":"A heat flow problem from Ericksen’s model for nematic liquid crystals with variable degree of orientation, II","authors":"Chi-Cheung Poon","doi":"10.4310/cag.2022.v30.n9.a5","DOIUrl":"https://doi.org/10.4310/cag.2022.v30.n9.a5","url":null,"abstract":"","PeriodicalId":50662,"journal":{"name":"Communications in Analysis and Geometry","volume":"1 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70404684","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01DOI: 10.4310/cag.2022.v30.n2.a5
Donghao Wang
{"title":"On finite energy monopoles on $C times Sigma$","authors":"Donghao Wang","doi":"10.4310/cag.2022.v30.n2.a5","DOIUrl":"https://doi.org/10.4310/cag.2022.v30.n2.a5","url":null,"abstract":"","PeriodicalId":50662,"journal":{"name":"Communications in Analysis and Geometry","volume":"1 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70404167","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01DOI: 10.4310/cag.2022.v30.n8.a6
Chuangqiang Hu, S. Yau, Huaiqing Zuo
{"title":"Complex structures of a twenty-dimensional family of Calabi–Yau $3$-folds","authors":"Chuangqiang Hu, S. Yau, Huaiqing Zuo","doi":"10.4310/cag.2022.v30.n8.a6","DOIUrl":"https://doi.org/10.4310/cag.2022.v30.n8.a6","url":null,"abstract":"","PeriodicalId":50662,"journal":{"name":"Communications in Analysis and Geometry","volume":"1 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70404563","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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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