%0 Journal Article %T Normal scalar curvature conjecture and its applications %A Zhiqin Lu %J Mathematics %D 2008 %I arXiv %R 10.1016/j.jfa.2011.05.002 %X In this paper, we proved the Normal Scalar Curvature Conjecture and the Bottcher-Wenzel Conjecture. We also established some new pinching theorems for minimal submanifolds in spheres. %U http://arxiv.org/abs/0803.0502v3