[en] This brief summary of a lecture contains discussions of smooth geometry, metric geometry, first applications of tensor calculus, geometry in geodesic spaces, and harmonic maps. 6 refs

[en] The paper discusses the solutions of the evolution equation for Riemannian manifolds M when dim M ≥ 2

No abstract available

[en] I. An abstract Dirichlet problem: Hilbert space background; Representation of functionals; Compact transformations; The Dirichlet problem. II. Elliptic operators on the torus: Group duality and Fourier analysis; The Hilbert spaces; Dirichlet's problem on Tsup(n); Regularity of solutions; Zero boundary values in IRsup(n); Strongly elliptic systems. III. Differential operators on vector bundles: Sheaves of modules; Vector bundles; Smooth manifolds and vector bundles; Certain operators on vector bundles; Riemannian structures; Differential operators. IV. The existence theorem and applications: The existence theorem; Hodge's theorem. (author)

[en] A key result on the boundedness of positive subsolutions of certain non-uniformly elliptic equations is established. 6 refs

[en] The paper deals with an improved flexible version of stochastic calculus (Ito, Gihman, McShane) applicable in describing flow processes as well as diffusion processes. The sections are: Introduction; the Wiener measure, stochastic integrals; stochastic integral equations; stochastic dynamical systems; applications (3 examples). (author)

[en] Here is an exposition of certain recent results deforming closed curves by heat flow. (author)