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An almost pluriclosed flow 几乎多元封闭的流
Geometric Flows Pub Date : 2017-01-27 DOI: 10.1515/geofl-2017-0002
Masaya Kawamura
{"title":"An almost pluriclosed flow","authors":"Masaya Kawamura","doi":"10.1515/geofl-2017-0002","DOIUrl":"https://doi.org/10.1515/geofl-2017-0002","url":null,"abstract":"Abstract We define two parabolic flows on almost complex manifolds, which coincide with the pluriclosed flow and the Hermitian curvature flow respectively on complex manifolds.We study the relationship between these parabolic evolution equations on compact almost Hermitian manifolds.","PeriodicalId":310900,"journal":{"name":"Geometric Flows","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133345024","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}
引用次数: 2
Motion by curvature of networks with two triple junctions 具有两个三重结点的网络的曲率运动
Geometric Flows Pub Date : 2016-06-26 DOI: 10.1515/geofl-2016-0002
C. Mantegazza, M. Novaga, Alessandra Pluda
{"title":"Motion by curvature of networks with two triple junctions","authors":"C. Mantegazza, M. Novaga, Alessandra Pluda","doi":"10.1515/geofl-2016-0002","DOIUrl":"https://doi.org/10.1515/geofl-2016-0002","url":null,"abstract":"Abstract We consider the evolution by curvature of a general embedded network with two triple junctions. We classify the possible singularities and we discuss the long time existence of the evolution.","PeriodicalId":310900,"journal":{"name":"Geometric Flows","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126827668","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}
引用次数: 18
Type-II singularities of two-convex immersed mean curvature flow 双凸浸没平均曲率流的ii型奇异性
Geometric Flows Pub Date : 2016-05-31 DOI: 10.1515/geofl-2016-0001
T. Bourni, Mathew T. Langford
{"title":"Type-II singularities of two-convex immersed mean curvature flow","authors":"T. Bourni, Mathew T. Langford","doi":"10.1515/geofl-2016-0001","DOIUrl":"https://doi.org/10.1515/geofl-2016-0001","url":null,"abstract":"Abstract We show that any strictly mean convex translator of dimension n ≥ 3 which admits a cylindrical estimate and a corresponding gradient estimate is rotationally symmetric. As a consequence, we deduce that any translating solution of the mean curvature flow which arises as a blow-up limit of a two-convex mean curvature flow of compact immersed hypersurfaces of dimension n ≥ 3 is rotationally symmetric. The proof is rather robust, and applies to a more general class of translator equations. As a particular application, we prove an analogous result for a class of flows of embedded hypersurfaces which includes the flow of twoconvex hypersurfaces by the two-harmonic mean curvature.","PeriodicalId":310900,"journal":{"name":"Geometric Flows","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125083564","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}
引用次数: 32
Anisotropic mean curvature on facets and relations with capillarity 面上各向异性平均曲率及其与毛细的关系
Geometric Flows Pub Date : 2015-09-04 DOI: 10.1515/geofl-2015-0005
Stefano Amato, G. Bellettini, L. Tealdi
{"title":"Anisotropic mean curvature on facets and relations with capillarity","authors":"Stefano Amato, G. Bellettini, L. Tealdi","doi":"10.1515/geofl-2015-0005","DOIUrl":"https://doi.org/10.1515/geofl-2015-0005","url":null,"abstract":"Abstract Given an anisotropy ɸ on R3, we discuss the relations between the ɸ-calibrability of a facet F ⊂ ∂E of a solid crystal E, and the capillary problem on a capillary tube with base F. When F is parallel to a facet ̃︀ BFɸ of the unit ball of ɸ, ɸ-calibrability is equivalent to show the existence of a ɸ-subunitary vector field in F, with suitable normal trace on @F, and with constant divergence equal to the ɸ-mean curvature of F. Assuming E convex at F, ̃︀ BFɸ a disk, and F (strictly) ɸ-calibrable, such a vector field is obtained by solving the capillary problem on F in absence of gravity and with zero contact angle. We show some examples of facets for which it is possible, even without the strict ɸ-calibrability assumption, to build one of these vector fields. The construction provides, at least for convex facets of class C1,1, the solution of the total variation flow starting at 1F.","PeriodicalId":310900,"journal":{"name":"Geometric Flows","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132228784","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}
引用次数: 6
A formal Riemannian structure on conformal classes and the inverse Gauss curvature flow 保形类和逆高斯曲率流上的正式黎曼结构
Geometric Flows Pub Date : 2015-07-16 DOI: 10.1515/geofl-2019-0003
M. Gursky, J. Streets
{"title":"A formal Riemannian structure on conformal classes and the inverse Gauss curvature flow","authors":"M. Gursky, J. Streets","doi":"10.1515/geofl-2019-0003","DOIUrl":"https://doi.org/10.1515/geofl-2019-0003","url":null,"abstract":"Abstract We define a formal Riemannian metric on a given conformal class of metrics with signed curvature on a closed Riemann surface. As it turns out this metric is the well-known Mabuchi-Semmes-Donaldson metric of Kähler geometry in a different guise. The metric has many interesting properties, and in particular we show that the classical Liouville energy is geodesically convex. This suggests a different approach to the uniformization theorem by studying the negative gradient flow of the normalized Liouville energy with respect to this metric, a new geometric flow whose principal term is the inverse of the Gauss curvature. We prove long time existence of solutions with arbitrary initial data and weak convergence to constant scalar curvature metrics by exploiting the metric space structure.","PeriodicalId":310900,"journal":{"name":"Geometric Flows","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123853441","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}
引用次数: 6
Singularities of relativistic membranes 相对论膜的奇点
Geometric Flows Pub Date : 2015-04-23 DOI: 10.1515/geofl-2015-0003
Jens Eggers, Jens Hoppe, Mariusz Hynek, Nugzar Suramlishvili
{"title":"Singularities of relativistic membranes","authors":"Jens Eggers, Jens Hoppe, Mariusz Hynek, Nugzar Suramlishvili","doi":"10.1515/geofl-2015-0003","DOIUrl":"https://doi.org/10.1515/geofl-2015-0003","url":null,"abstract":"Abstract Pointing out a crucial relation with caustics of the eikonal equation we discuss the singularity formation of 2-dimensional surfaces that sweep out 3-manifolds of zero mean curvature in R3,1.","PeriodicalId":310900,"journal":{"name":"Geometric Flows","volume":"121 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123224437","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}
引用次数: 17
The area preserving curve shortening flow with Neumann free boundary conditions 具有Neumann自由边界条件的保面积曲线缩短流
Geometric Flows Pub Date : 2015-03-19 DOI: 10.1515/geofl-2015-0004
Elena Mäder-Baumdicker
{"title":"The area preserving curve shortening flow with Neumann free boundary conditions","authors":"Elena Mäder-Baumdicker","doi":"10.1515/geofl-2015-0004","DOIUrl":"https://doi.org/10.1515/geofl-2015-0004","url":null,"abstract":"Abstract We study the area preserving curve shortening flow with Neumann free boundary conditions outside of a convex domain in the Euclidean plane. Under certain conditions on the initial curve the flow does not develop any singularity, and it subconverges smoothly to an arc of a circle sitting outside of the given fixed domain and enclosing the same area as the initial curve.","PeriodicalId":310900,"journal":{"name":"Geometric Flows","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126406809","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}
引用次数: 4
Evolution of convex entire graphs by curvature flows 曲率流的凸整图演化
Geometric Flows Pub Date : 2015-01-03 DOI: 10.1515/geofl-2015-0006
R. Alessandroni, C. Sinestrari
{"title":"Evolution of convex entire graphs by curvature flows","authors":"R. Alessandroni, C. Sinestrari","doi":"10.1515/geofl-2015-0006","DOIUrl":"https://doi.org/10.1515/geofl-2015-0006","url":null,"abstract":"Abstract We consider the evolution of an entire convex graph in euclidean space with speed given by a symmetric function of the principal curvatures. Under suitable assumptions on the speed and on the initial data, we prove that the solution exists for all times and it remains a graph. In addition, after appropriate rescaling, it converges to a homothetically expanding solution of the flow. In this way, we extend to a class of nonlinear speeds the well known results of Ecker and Huisken for the mean curvature flow.","PeriodicalId":310900,"journal":{"name":"Geometric Flows","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128144375","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}
引用次数: 4
Gradient estimates for inverse curvature flows in hyperbolic space 双曲空间中逆曲率流的梯度估计
Geometric Flows Pub Date : 2014-10-06 DOI: 10.1515/geofl-2015-0002
Julian Scheuer
{"title":"Gradient estimates for inverse curvature flows in hyperbolic space","authors":"Julian Scheuer","doi":"10.1515/geofl-2015-0002","DOIUrl":"https://doi.org/10.1515/geofl-2015-0002","url":null,"abstract":"Abstract We prove gradient estimates for hypersurfaces in the hyperbolic space Hn+1, expanding by negative powers of a certain class of homogeneous curvature functions F. We obtain optimal gradient estimates for hypersurfaces evolving by certain powers p > 1 of F-1 and smooth convergence of the properly rescaled hypersurfaces. In particular, the full convergence result holds for the inverse Gauss curvature flow of surfaces without any further pinching condition besides convexity of the initial hypersurface.","PeriodicalId":310900,"journal":{"name":"Geometric Flows","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132617223","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}
引用次数: 18
A convergence result for the Gradient Flow of ∫ |A|2 in Riemannian Manifolds 黎曼流形中∫|A|2梯度流的收敛性结果
Geometric Flows Pub Date : 2014-05-12 DOI: 10.1515/geofl-2015-0001
A. Magni
{"title":"A convergence result for the Gradient Flow of ∫ |A|2 in Riemannian Manifolds","authors":"A. Magni","doi":"10.1515/geofl-2015-0001","DOIUrl":"https://doi.org/10.1515/geofl-2015-0001","url":null,"abstract":"Abstract We study the gradient flow of the L2−norm of the second fundamental form for smooth immersions of two-dimensional surfaces into compact Riemannian manifolds. By analogy with the results obtained in [10] and [11] for the Willmore flow, we prove lifespan estimates in terms of the L2−concentration of the second fundamental form of the initial data and we show the existence of blowup limits. Under special condition both on the initial data and on the target manifold, we prove a long time existence result for the flow and the subconvergence to a critical immersion.","PeriodicalId":310900,"journal":{"name":"Geometric Flows","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127262399","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}
引用次数: 1
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