Frobenius-type theorems for Lipschitz distributions

We generalize the classical Frobenius Theorem to distributions that are spanned by locally Lipschitz vector fields. The various versions of the involutivity conditions are extended by means of set-valued Lie derivatives—in particular, set-valued Lie brackets—and set-valued exterior derivatives. A PDEs counterpart of these Frobenius-type results is investigated as well.     

Heat content and Hardy inequality for complete Riemannian manifolds

Upper bounds are obtained for the heat content of an open set D in a complete Riemannian manifold, provided the Dirichlet-Laplace-Beltrami operator satisfies a strong Hardy inequality, and the distance function on D satisfies an integrability condition.     

The Hörmander and Maslov Classes and Fomenko's Conjecture

Some functorial properties are studied for the Hörmander classes defined for symplectic bundles. The behavior of the Chern first form on a Lagrangian submanifold in an almost Hermitian manifold is also studied, and Fomenko's conjecture about the behavior of a Maslov class on minimal Lagrangian submanifolds is considered.     

弱阻尼KdV方程样条小波基下约化形式的弱解

本文研究弱阻尼ＫｄＶ方程样条小波基下约化形式的弱解·     

BIFURCATIONS TO A HETEROCLINIC MANIFOLD WITH NONHYPERBOLIC EQUILIBRIA IN R~n

1IntroductionAsiswellkllowll,11eteroclillicalld11olllo(.lillicorbitsplayallilllportalltroleilltilequalitativetheoryofdyualllicalsystellis.Dyualllicalsystelliswitlla11etcroclinicor11ollloclinicorbitoftenexhibitacolllplicatedglobalbehaviour.UPtoflow.alotofworkhasbeeddolleonbifurcationsofheteroclinicand11omoclillicorbitsconnectillg11yperbolicequilibriumpointsinn-dimensiollaldynalllicaJsystellls.See,l'Orexalllple,[1-3,andreferellcesthereinl.Morerecentlyinterest11asbeedpaidtobifurcationsofhetcroc…     

On G-Trace and G-Index in Deformation Quantization

For a compact group G of symplectomorphisms we define a G-trace on the algebra of quantum observables by postulating its properties. We give an explicit construction of such a trace and prove a G-index theorem similar to the Atiyah–Segal–Singer equivariant index theorem for elliptic operators.     

光滑流形的迹上的W^m,p（Ω）嵌入定理

本文讨论了将嵌入定理推广到光滑流形的迹上去,并证有了强局部Lipschitz性质下的嵌入定理.     

Problems on Bieberbach Groups and Flat Manifolds

We present about twenty conjectures, problems and questions about flat manifolds. Many of them build the bridges between the flat world and representation theory of the finite groups, hyperbolic geometry and dynamical systems. In memory of Charles B. Thomas     

4-dimensional anti-Kähler manifolds

We show that every 4-dimensional anti-Kähler manifold is Einstein and locally symmetric. In particular any 4-dimensional anti-Kähler manifold with zero scalar curvature is flat.     

Alexandrov Par Excellence

This is a short tribute to Alexandr Alexandrov (1912–1999).