Locally flat, locally tame, and tame embeddings

Locally Tame Curves and Surfaces in Three-dimensional Manifolds

Tame Flows

The tame flows are “nice” flows on “nice” spaces. The nice (tame) sets are the pfaffian sets introduced by Khovanski, and a flow Φ : R×X → X on pfaffian set X is tame if the graph of Φ is a pfaffian subset of R×X×X . Any compact tame set admits plenty tame flows. We prove that the flow determined by the gradient of a generic real analytic function with respect to a generic real analytic metric ...

Tame structures

We study various notions of “tameness” for definably complete expansions of ordered fields. We mainly study structures with locally o-minimal open core, d-minimal structures, and dense pairs of d-minimal structures.

Embeddings of Locally Connected Compacta

Let A' be a ^-dimensional compactum and /: X -» M" a map into a piecewise linear n-manifold. n > k + 3. The main result of this paper asserts that if X is locally (2k ^-connected and / is (2k n + l)-connected, then / is homotopic to a CE equivalence. In particular, every ^--dimensional, /-connected, locally /--connected compactum is CE equivalent to a compact subset of R2*~r as long as r < k 3....

On a class of locally projectively flat Finsler metrics

‎In this paper we study Finsler metrics with orthogonal invariance‎. ‎We‎ ‎find a partial differential equation equivalent to these metrics being locally projectively flat‎. ‎Some applications are given‎. ‎In particular‎, ‎we give an explicit construction of a new locally projectively flat Finsler metric of vanishing flag curvature which differs from the Finsler metric given by Berwald in 1929.