In this paper,we compute the adiabatic limit of the scalar curvature and prove several vanishing theorems by taking adiabatic limits.As an application,we give a Kastler-Kalau-Walze type theorem for foliations.
We provide two new positive mass theorems under respective modified energy conditions allowing T00 negative on some compact set for certain modified asymptotically hyperbolic manifolds. This work is analogous to Zhang...We provide two new positive mass theorems under respective modified energy conditions allowing T00 negative on some compact set for certain modified asymptotically hyperbolic manifolds. This work is analogous to Zhang’s previous result for modified asymptotically flat initial data sets.展开更多
基金partially supported by the National Natural Science Foundation of China (Grant No. 10421001)the National Key Basic Research Project of China (Grant No. 2006CB805905)the Innovation Project ofChinese Academy of Sciences
文摘We extend our previous definition of quasi-local mass to 2-spheres whose Gauss curvature is negative, and prove its positivity.
基金supported by National Natural Science Foundation of USA(Grant No.DMS0705284)National Natural Science Foundation of China(Grant No.10801027)
文摘In this paper,we compute the adiabatic limit of the scalar curvature and prove several vanishing theorems by taking adiabatic limits.As an application,we give a Kastler-Kalau-Walze type theorem for foliations.
文摘We provide two new positive mass theorems under respective modified energy conditions allowing T00 negative on some compact set for certain modified asymptotically hyperbolic manifolds. This work is analogous to Zhang’s previous result for modified asymptotically flat initial data sets.
