COMPARISON THEOREMS FOR THE VOLUMES OF TUBES ABOUT METRIC BALLS IN CAT(·)-SPACES

• 발행기관: 충청수학회
• 저자명: Doohann Lee Yong-Il Kim
• 간행물 정보: 『Journal of the Chungcheong Mathematical Society』Volume 24, No. 3, 457~467쪽, 전체 11쪽
• 주제분류: 자연과학 > 자연과학일반
• 파일형태: PDF
• 발행일자: 2011.08.30

영문 초록

In this paper, we establish some comparison theorems about volumes of tubes in metric spaces with nonpositive curva-ture. First we compare the Hausdor？？ measure of tube about a metric ball contained in an (n ¡ 1)-dimensional totally geodesic subspace of an n-dimensional locally compact, geodesically com-plete Hadamard space with Lebesgue measure of its corresponding tube in Euclidean space Rn, and then develop the result to the case of an m-dimensional totally geodesic subspace for 1 < m < n with additional condition. Also, we estimate the Hausdor？？ measure of the tube about a shortest curve in a metric space of curvature bounded above and below.

목차

1. Introduction

2. Main results