Continuous, SL(n) and translation invariant real-valued valuations on Sobolev spaces are classified.The centro-affine Hadwiger's theorem is applied. In the homogeneous case, these valuations turn out to be L^p-nor...Continuous, SL(n) and translation invariant real-valued valuations on Sobolev spaces are classified.The centro-affine Hadwiger's theorem is applied. In the homogeneous case, these valuations turn out to be L^p-norms raised to p-th power(up to suitable multipication scales).展开更多
基金supported by Austrian Science Fund Project(Grant No.P23639-N18)National Natural Science Foundation of China(Grant No.11371239)
文摘Continuous, SL(n) and translation invariant real-valued valuations on Sobolev spaces are classified.The centro-affine Hadwiger's theorem is applied. In the homogeneous case, these valuations turn out to be L^p-norms raised to p-th power(up to suitable multipication scales).
