Differential Geometry and its Applications最新文献_第10页

Some characterizations of Bach solitons via Ricci curvature 利用Ricci曲率刻画巴赫孤子

IF 0.5 4区数学

Differential Geometry and its Applications Pub Date : 2023-10-01 DOI: 10.1016/j.difgeo.2023.102046

Antonio W. Cunha , Eudes L. de Lima , Rong Mi

引用次数: 2

Equidistant sets on Alexandrov surfaces 亚历山德罗夫曲面上的等距集

IF 0.5 4区数学

Differential Geometry and its Applications Pub Date : 2023-10-01 DOI: 10.1016/j.difgeo.2023.102042

Logan S. Fox, J.J.P. Veerman

引用次数: 1

Geometry of sample spaces 样本空间几何

IF 0.5 4区数学

Differential Geometry and its Applications Pub Date : 2023-10-01 DOI: 10.1016/j.difgeo.2023.102029

Philipp Harms , Peter W. Michor , Xavier Pennec , Stefan Sommer

{"title":"Geometry of sample spaces","authors":"Philipp Harms , Peter W. Michor , Xavier Pennec , Stefan Sommer","doi":"10.1016/j.difgeo.2023.102029","DOIUrl":"10.1016/j.difgeo.2023.102029","url":null,"abstract":"<div>In statistics, independent, identically distributed random samples do not carry a natural ordering, and their statistics are typically invariant with respect to permutations of their order. Thus, an n-sample in a space M can be considered as an element of the quotient space of <math><msup><mrow><mi>M</mi></mrow><mrow><mi>n</mi></mrow></msup></math> modulo the permutation group. The present paper takes this definition of sample space and the related concept of orbit types as a starting point for developing a geometric perspective on statistics. We aim at deriving a general mathematical setting for studying the behavior of empirical and population means in spaces ranging from smooth Riemannian manifolds to general stratified spaces.We fully describe the orbifold and path-metric structure of the sample space when M is a manifold or path-metric space, respectively. These results are non-trivial even when M is Euclidean. We show that the infinite sample space exists in a Gromov–Hausdorff type sense and coincides with the Wasserstein space of probability distributions on M. We exhibit Fréchet means and k-means as metric projections onto 1-skeleta or k-skeleta in Wasserstein space, and we define a new and more general notion of polymeans. This geometric characterization via metric projections applies equally to sample and population means, and we use it to establish asymptotic properties of polymeans such as consistency and asymptotic normality.</div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47108488","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}

引用次数: 3

Existence of Lie algebroids on the tangent bundle with a given anchor map of constant rank 给定常秩锚映射的切束上李代数群的存在性

IF 0.5 4区数学

Differential Geometry and its Applications Pub Date : 2023-10-01 DOI: 10.1016/j.difgeo.2023.102040

J. Monterde

引用次数: 0

Existence of a variational principle for PDEs with symmetries and current conservation 具有对称性和电流守恒的偏微分方程变分原理的存在性

IF 0.5 4区数学

Differential Geometry and its Applications Pub Date : 2023-10-01 DOI: 10.1016/j.difgeo.2023.102004

Markus Dafinger

{"title":"Existence of a variational principle for PDEs with symmetries and current conservation","authors":"Markus Dafinger","doi":"10.1016/j.difgeo.2023.102004","DOIUrl":"https://doi.org/10.1016/j.difgeo.2023.102004","url":null,"abstract":"<div>It is well-known from Noether's theorem that symmetries of a variational functional lead to conservation laws of the corresponding Euler-Lagrange equation. We reverse this statement and prove that a differential equation, which satisfies sufficiently many symmetries and corresponding conservation laws, leads to a variational functional, whose Euler-Lagrange equation is the given differential equation. Sufficiently many symmetries means that the set of symmetry vector fields satisfy span<math><mo>{</mo><msub><mrow><mi>V</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>:</mo><mi>V</mi><mo>∈</mo><mtext>Sym</mtext><mo>}</mo><mo>=</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>p</mi></mrow></msub><mi>E</mi></math>, that is, they span the tangent space <math><msub><mrow><mi>T</mi></mrow><mrow><mi>p</mi></mrow></msub><mi>E</mi></math> at each point p of a fiber bundle E, which describes the dependent- and independent coordinates. Higher order coordinates are described by the jet bundle <math><msup><mrow><mi>J</mi></mrow><mrow><mi>k</mi></mrow></msup><mi>E</mi></math> and we require no span-assumptions on <math><mi>T</mi><msup><mrow><mi>J</mi></mrow><mrow><mi>k</mi></mrow></msup><mi>E</mi></math>. Our main theorem states that Noether's theorem can be reversed in this sense for second order differential equations, or more precisely, for so-called second order source forms on <math><msup><mrow><mi>J</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>E</mi></math>, which are required to write the differential equation as a weak formulation (every Euler-Lagrange equation is derived from a first variation, that is, from a weak formulation). Counter examples show that our theorem is sharp.</div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49760057","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}

引用次数: 0

Real hypersurfaces of nonflat complex space forms with weakly transversal Killing operators 具有弱横向kill算子的非平坦复空间形式的实超曲面

IF 0.5 4区数学

Differential Geometry and its Applications Pub Date : 2023-09-28 DOI: 10.1016/j.difgeo.2023.102061

Zejun Hu, Xi Zhang

引用次数: 0

On isoperimetric problem in 2-dimensional Randers space 二维Randers空间中的等周问题

IF 0.5 4区数学

Differential Geometry and its Applications Pub Date : 2023-09-28 DOI: 10.1016/j.difgeo.2023.102062

Hongmei Zhu , Ranran Li

引用次数: 0

Some geometric properties of normal and tangent submanifolds 正规和正切子流形的一些几何性质

IF 0.5 4区数学

Differential Geometry and its Applications Pub Date : 2023-09-27 DOI: 10.1016/j.difgeo.2023.102063

Josué Meléndez, Eduardo Rodríguez-Romero

引用次数: 0

Harmonic G2-structures on almost Abelian Lie groups 几乎阿贝尔李群上的调和g2结构

IF 0.5 4区数学

Differential Geometry and its Applications Pub Date : 2023-09-19 DOI: 10.1016/j.difgeo.2023.102060

Andrés J. Moreno

引用次数: 1

Homogeneous nonlinear splittings and Finsler submersions 齐次非线性分裂和Finsler淹没

IF 0.5 4区数学

Differential Geometry and its Applications Pub Date : 2023-08-17 DOI: 10.1016/j.difgeo.2023.102049

S. Hajdú, T. Mestdag

引用次数: 2