Ⅲ-nitride light-emitting diodes(LEDs)are now used almost everywhere,due to their energy-saving capability.In the near future,the vast majority of lighting sources will undoubtedly be based on LEDs.What future technol...Ⅲ-nitride light-emitting diodes(LEDs)are now used almost everywhere,due to their energy-saving capability.In the near future,the vast majority of lighting sources will undoubtedly be based on LEDs.What future technologies and applications can we expect from Ⅲ-nitride-based and particularly gallium nitride(Ga N)-based,materials and devices?展开更多
In this note we present various extensions of Obata’s rigidity theorem concerning the Hessian of a function on a Riemannian manifold.They include general rigidity theorems for the generalized Obata equation,and hyper...In this note we present various extensions of Obata’s rigidity theorem concerning the Hessian of a function on a Riemannian manifold.They include general rigidity theorems for the generalized Obata equation,and hyperbolic and Euclidean analogs of Obata’s theorem.Besides analyzing the full rigidity case,we also characterize the geometry and topology of the underlying manifold in more general situations.展开更多
文摘Ⅲ-nitride light-emitting diodes(LEDs)are now used almost everywhere,due to their energy-saving capability.In the near future,the vast majority of lighting sources will undoubtedly be based on LEDs.What future technologies and applications can we expect from Ⅲ-nitride-based and particularly gallium nitride(Ga N)-based,materials and devices?
文摘In this note we present various extensions of Obata’s rigidity theorem concerning the Hessian of a function on a Riemannian manifold.They include general rigidity theorems for the generalized Obata equation,and hyperbolic and Euclidean analogs of Obata’s theorem.Besides analyzing the full rigidity case,we also characterize the geometry and topology of the underlying manifold in more general situations.