We study the set where the so-called Bergman representative coordinates (or Bergman functions) form an immersion. We provide an estimate of the size of a maximal geodesic ball with respect to the Bergman metric contai...We study the set where the so-called Bergman representative coordinates (or Bergman functions) form an immersion. We provide an estimate of the size of a maximal geodesic ball with respect to the Bergman metric contained in this set. By concrete examples we show that these estimates are the best possible.展开更多
Let Pt denote the tubular hypersurface of radius t around a given compatible submanifold in a symmetric space of arbitrary rank. The authors will obtain some relations between the integrated mean curvatures of P, and ...Let Pt denote the tubular hypersurface of radius t around a given compatible submanifold in a symmetric space of arbitrary rank. The authors will obtain some relations between the integrated mean curvatures of P, and their derivatives with respect to f. Moreover, the authors will emphasize the differences between the results obtained for rank one and arbitrary rank symmetric spaces.展开更多
We study the volume growth of the geodesic balls of a minimal submanifold in a Euclidean space.A necessary condition for the isometric minimal immersion into a Euclidean space is obtained. A classification of non-posi...We study the volume growth of the geodesic balls of a minimal submanifold in a Euclidean space.A necessary condition for the isometric minimal immersion into a Euclidean space is obtained. A classification of non-positively curved minimal hypersurfaces in a Euclidean space is given.展开更多
文摘We study the set where the so-called Bergman representative coordinates (or Bergman functions) form an immersion. We provide an estimate of the size of a maximal geodesic ball with respect to the Bergman metric contained in this set. By concrete examples we show that these estimates are the best possible.
文摘Let Pt denote the tubular hypersurface of radius t around a given compatible submanifold in a symmetric space of arbitrary rank. The authors will obtain some relations between the integrated mean curvatures of P, and their derivatives with respect to f. Moreover, the authors will emphasize the differences between the results obtained for rank one and arbitrary rank symmetric spaces.
基金This work is partially supported by the National Science Foundation of China
文摘We study the volume growth of the geodesic balls of a minimal submanifold in a Euclidean space.A necessary condition for the isometric minimal immersion into a Euclidean space is obtained. A classification of non-positively curved minimal hypersurfaces in a Euclidean space is given.
