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Ashtekar-Kodama Gravity as a Classical and Quantum Extension of Loop Quantum Gravity: 《Journal of Modern Physics》2024年第6期864-937,共74页Jan Helm; This paper presents a new theory of gravity, called here Ashtekar-Kodama (AK) gravity, which is based on the Ashtekar-Kodama formulation of loop quantum gravity (LQG), yields in the limit the Einstein equations, and i...; 关键词：Quantum Gravity Loop Quantum Gravity General Relativity Gravitational Wave Gauge Field Theory Graviton Hamiltonian Constraint Gaussian Constraint Diffeomorphism Constraint

Topology and Curvature of Isoparametric Families in Spheres: 《Communications in Mathematics and Statistics》2023年第2期439-475,共37页Chao Qian Zizhou Tang Wenjiao Yan; partially supported by the NSFC(Nos.11722101,11871282,11931007);BNSF(Z190003);Nankai Zhide Foundation;Beijing Institute of Technology Research Fund Program for Young Scholars.; An isoparametric family in the unit sphere consists of parallel isoparametric hypersurfaces and their two focal submanifolds.The present paper has two parts.The first part investigates topology of the isoparametric fa...; 关键词：Isoparametric hypersurface Focal submanifold Homotopy equivalent HOMEOMORPHISM DIFFEOMORPHISM Parallelizability Lusternik-Schnirelmann category Sectional curvature Ricci curvature

Finite Diffeomorphism Types of Four Dimensional Ricci Flow with Bounded Scalar Curvature: 《Acta Mathematica Sinica,English Series》2021年第11期1751-1767,共17页Wen Shuai JIANG; Supported by NSFC (Grant No. 11701507);the Fundamental Research Funds for the Central Universities 2019QNA3001 and DECRA 190101471。; In this paper,we consider Ricci flow on four dimensional closed manifold with bounded scalar curvature,noncollasping volume and bounded diameter.Under such conditions,we can show that the manifold has finitely many di...; 关键词：Ricci flow scalar curvature

A Note on the Stability of Geodesics on Diffeomorphism Groups with One-side Invariant Metric: 《Acta Mathematica Sinica,English Series》2020年第5期620-630,共11页Li Juan ZHOU; supported by Education Department of Inner Mongolia Autonomous Region(Grant No.NJZY20004);NSFC(Grant No.11671392)。; In this note,we consider the stability of geodesics on volume-preserving diffeomorphism groups with one-side invariant metric.We showed that for non-Beltrami fields on a three-dimensional compact manifold,there does n...; 关键词：Volume-preserving DIFFEOMORPHISM GROUP Bott-Virasoro GROUP Euler equation GEODESIC Eulerian INSTABILITY Lagrangian INSTABILITY

A generalized π2-diffeomorphism finiteness theorem被引量：1: 《Frontiers of Mathematics in China》2020年第2期399-418,共20页Xiaochun RONG Xuchao YAO; Theπ2-diffeomorphism finiteness result of F.Fang-X.Rong and A.Petrunin-W.Tuschmann(independently)asserts that the diffeomorphic types of compact n-manifolds M with vanishing first and second homotopy groups can be bo...; 关键词：Collapsing with bounded sectional curvature diffeomorphism finiteness vanishing second homotopy group

Kobayashi’s and Teichmuller’s Metrics and Bers Complex Manifold Structure on Circle Diffeomorphisms被引量：1: 《Acta Mathematica Sinica,English Series》2020年第3期245-272,共28页Yun Ping JIANG; supported by the National Science Foundation;supported by a collaboration grant from the Simons Foundation(Grant No.523341);PSC-CUNY awards and a grant from NSFC(Grant No.11571122)。; Given a modulus of continuity ω,we consider the Teichmuller space TC1+ω as the space of all orientation-preserving circle diffeomorphisms whose derivatives are ω-continuous functions modulo the space of Mobius tran...; 关键词：Bers complex manifold STRUCTURE circle DIFFEOMORPHISM modulus of continuity quasisymmetric circle HOMEOMORPHISM Teichmuller space Kobayashi's METRIC Teichmuller's METRIC

Diffeomorphisms with the M0-shadowing Property: 《Acta Mathematica Sinica,English Series》2019年第11期1760-1770,共11页Xu ZHANG Xin Xing WU; Supported by the National Natural Science Foundation of China(Grant Nos.11601449 and 11701328);Science and Technology Innovation Team of Education Department of Sichuan for Dynamical System and its Applications(Grant No.18TD0013);Youth Science and Technology Innovation Team of Southwest Petroleum University for Nonlinear Systems(Grant No.2017CXTD02);Scientific Research Starting Project of Southwest Petroleum University(Grant No.2015QHZ029);Shandong Provincial Natural Science Foundation,China(Grant No.ZR2017QA006);Young Scholars Program of Shandong University,Weihai(Grant No.2017WHWLJH09); This paper studies the M0-shadowing property for the dynamics of diffeomorphisms defined on closed manifolds. The C1 interior of the set of all two dimensional diffeomorphisms with the M0-shadowing property is describ...; 关键词：Anosov DIFFEOMORPHISM AVERAGE SHADOWING PROPERTY Mα-shadowing

Existence of Invariant Tori in Reversible Mappings: 《Acta Mathematica Sinica,English Series》2019年第9期1419-1452,共34页Sheng Qing HU; In this paper, we study reversible diffeomorphisms with n angular variables and only one action variable. Under some reasonable non-degeneracy conditions, we prove that the reversible diffeomorphisms sufficiently clos...; 关键词：REVERSIBLE DIFFEOMORPHISM invariant TORI NON-DEGENERACY conditions KAM method

Finite Determinacy of High Codimension Smooth Function Germs: 《Applied Mathematics(A Journal of Chinese Universities)》2019年第1期92-99,共8页GAN Wen-liang PEI Dong-he LI Qiang GAO Rui-mei; Supported by the National Natural Science Foundation of China(11671070,11501051);NSF of Heilongjiang Province of China(QC2016008);the Project of Science and Technology of Jilin Provincial Education Department(JJKH2090547KJ); Mather gave the necessary and suffcient conditions for the ?nite determinacy smooth function germs with no more than codimension 4. The theorem is very effective on determining low codimension smooth function germs. I...; 关键词：function GERM JACOBIAN ideal DIFFEOMORPHISM right EQUIVALENCE

Generalized Inverse Analysis on the Domain ?(A, A^+) in B(E,F)被引量：1: 《Analysis in Theory and Applications》2018年第2期127-134,共8页Zhaofeng Ma; Let B(E,F) be the set of all bounded linear operators from a Banach space E into another Banach space F,B^+(E, F) the set of all double splitting operators in B(E, F)and GI(A) the set of generalized inverses of A ∈ B...; 关键词：GENERALIZED INVERSE analysis SMOOTH DIFFEOMORPHISM SMOOTH SUBMANIFOLD

DIFFEOMORPHISM