2 research outputs found
On the volume growth and the topology of complete minimal submanifolds of a Euclidean space
Let be a -dimensional complete properly immersed minimal submanifold of a Euclidean space. We show that the number of the ends of is bounded above by k=\sup{\roman{volume}(M\cap B(t)) \over ω_nt^n}, where is the ball of the Euclidean space of center 0 and radius , is the volume of -dimensional unit Euclidean ball. Moreover, we prove that the number of ends of is equal to under some curvature decay condition