Pub Date : 2020-10-15DOI: 10.1007/s12220-020-00532-w
Kenneth D. Koenig, J. McNeal
{"title":"Percolation of Estimates for $${{bar{partial }}}$$ by the Method of Alternating Projections","authors":"Kenneth D. Koenig, J. McNeal","doi":"10.1007/s12220-020-00532-w","DOIUrl":"https://doi.org/10.1007/s12220-020-00532-w","url":null,"abstract":"","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":"1 1","pages":"1-19"},"PeriodicalIF":1.1,"publicationDate":"2020-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s12220-020-00532-w","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46971668","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 : 2020-09-08DOI: 10.1007/s12220-020-00501-3
G. Dafni, Ryan Gibara, Hong Yue
{"title":"Geometric Maximal Operators and $$mathrm {{BMO}}{}{}{}$$ on Product Bases","authors":"G. Dafni, Ryan Gibara, Hong Yue","doi":"10.1007/s12220-020-00501-3","DOIUrl":"https://doi.org/10.1007/s12220-020-00501-3","url":null,"abstract":"","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":"1 1","pages":"1-26"},"PeriodicalIF":1.1,"publicationDate":"2020-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s12220-020-00501-3","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41545541","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 : 2020-07-25DOI: 10.1007/s12220-020-00457-4
Ammar Khanfer, K. Lancaster
{"title":"Boundary Behavior of Rotationally Symmetric Prescribed Mean Curvature Hypersurfaces in $$pmb {varvec{{mathbb {R}}}}^{4}$$","authors":"Ammar Khanfer, K. Lancaster","doi":"10.1007/s12220-020-00457-4","DOIUrl":"https://doi.org/10.1007/s12220-020-00457-4","url":null,"abstract":"","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":"1 1","pages":"1-10"},"PeriodicalIF":1.1,"publicationDate":"2020-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s12220-020-00457-4","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46085834","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 : 2020-01-27DOI: 10.1007/s12220-020-00359-5
Lars Simon, Berit Stensønes
{"title":"An Example on s-H-Convexity in $$pmb {mathbb {C}^2}$$","authors":"Lars Simon, Berit Stensønes","doi":"10.1007/s12220-020-00359-5","DOIUrl":"https://doi.org/10.1007/s12220-020-00359-5","url":null,"abstract":"","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":"1 1","pages":"1-16"},"PeriodicalIF":1.1,"publicationDate":"2020-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s12220-020-00359-5","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45999407","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 : 2020-01-01Epub Date: 2019-01-23DOI: 10.1007/s12220-018-00137-4
Shantanu Dave, Stefan Haller
The short-time heat kernel expansion of elliptic operators provides a link between local and global features of classical geometries. For many geometric structures related to (non-)involutive distributions, the natural differential operators tend to be Rockland, hence hypoelliptic. In this paper, we establish a universal heat kernel expansion for formally self-adjoint non-negative Rockland differential operators on general closed filtered manifolds. The main ingredient is the analysis of parametrices in a recently constructed calculus adapted to these geometric structures. The heat expansion implies that the new calculus, a more general version of the Heisenberg calculus, also has a non-commutative residue. Many of the well-known implications of the heat expansion such as, the structure of the complex powers, the heat trace asymptotics, the continuation of the zeta function, as well as Weyl's law for the eigenvalue asymptotics, can be adapted to this calculus. Other consequences include a McKean-Singer type formula for the index of Rockland differential operators. We illustrate some of these results by providing a more explicit description of Weyl's law for Rumin-Seshadri operators associated with curved BGG sequences over 5-manifolds equipped with a rank-two distribution of Cartan type.
{"title":"The Heat Asymptotics on Filtered Manifolds.","authors":"Shantanu Dave, Stefan Haller","doi":"10.1007/s12220-018-00137-4","DOIUrl":"10.1007/s12220-018-00137-4","url":null,"abstract":"<p><p>The short-time heat kernel expansion of elliptic operators provides a link between local and global features of classical geometries. For many geometric structures related to (non-)involutive distributions, the natural differential operators tend to be Rockland, hence hypoelliptic. In this paper, we establish a universal heat kernel expansion for formally self-adjoint non-negative Rockland differential operators on general closed filtered manifolds. The main ingredient is the analysis of parametrices in a recently constructed calculus adapted to these geometric structures. The heat expansion implies that the new calculus, a more general version of the Heisenberg calculus, also has a non-commutative residue. Many of the well-known implications of the heat expansion such as, the structure of the complex powers, the heat trace asymptotics, the continuation of the zeta function, as well as Weyl's law for the eigenvalue asymptotics, can be adapted to this calculus. Other consequences include a McKean-Singer type formula for the index of Rockland differential operators. We illustrate some of these results by providing a more explicit description of Weyl's law for Rumin-Seshadri operators associated with curved BGG sequences over 5-manifolds equipped with a rank-two distribution of Cartan type.</p>","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":"30 1","pages":"337-389"},"PeriodicalIF":1.1,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6994647/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"37647622","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-01-01Epub Date: 2019-01-14DOI: 10.1007/s12220-018-00130-x
Volker Branding
Motivated from the action functional for bosonic strings with extrinsic curvature term we introduce an action functional for maps between Riemannian manifolds that interpolates between the actions for harmonic and biharmonic maps. Critical points of this functional will be called interpolating sesqui-harmonic maps. In this article we initiate a rigorous mathematical treatment of this functional and study various basic aspects of its critical points.
{"title":"On Interpolating Sesqui-Harmonic Maps Between Riemannian Manifolds.","authors":"Volker Branding","doi":"10.1007/s12220-018-00130-x","DOIUrl":"https://doi.org/10.1007/s12220-018-00130-x","url":null,"abstract":"<p><p>Motivated from the action functional for bosonic strings with extrinsic curvature term we introduce an action functional for maps between Riemannian manifolds that interpolates between the actions for harmonic and biharmonic maps. Critical points of this functional will be called interpolating sesqui-harmonic maps. In this article we initiate a rigorous mathematical treatment of this functional and study various basic aspects of its critical points.</p>","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":"30 1","pages":"248-273"},"PeriodicalIF":1.1,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s12220-018-00130-x","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"37647621","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-01-01DOI: 10.1007/978-3-030-34953-0_4
T. Colding, W. Minicozzi
{"title":"Analytical Properties for Degenerate Equations","authors":"T. Colding, W. Minicozzi","doi":"10.1007/978-3-030-34953-0_4","DOIUrl":"https://doi.org/10.1007/978-3-030-34953-0_4","url":null,"abstract":"","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":"73 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85827990","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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