Neighborhoods of Leviq-convex domains

Research paper by Viorel Vâjâitu

Indexed on: 01 Jan '98Published on: 01 Jan '98Published in: The Journal of Geometric Analysis


We consider bounded and q-complete domains inCnwithC2boundary. We show that they enjoy special q-convexity properties, i.e., they admit q-convex bounded exhaustion function and their closure do have a fundamental system of (q + 1)-complete neighborhoods. Moreover, we produce an example of a q- complete domain (which we called the q-worm) with smooth boundary whose closure does not possess a fundamental system of q-complete neighborhoods.Finally, extensions of these results to p-complete manifolds are given.