The $$L_p$$ Gauss image problem

The logarithmic Minkowski conjecture and the Lp-Minkowski problem

“…The Alexandrov problem; namely, the charaterization of C K,0 has been solved by Aleksandrov [4,5] (see also Oliker [215] and Bertrand [27] Böröczky, Lutwak, Yang, Zhang, Zhao [53]). For the L p version of the Alexandrov problem posed by Huang, Lutwak, Yang, Zhang [149], see for example Zhao [250], Li, Sheng, Ye, Yi [180] Mui [209] and Wu, Wu, Xiang [240]. If q = 0, n, then the following results are known:…”

The Logarithmic Minkowski conjecture and the $L_p$-Minkowski Problem

“…The Alexandrov problem; namely, the charaterization of C K,0 has been solved by Aleksandrov [4,5] (see also Böröczky, Lutwak, Yang, Zhang, Zhao [52], and for L p version of the Alexandrov problem posed by Huang, Lutwak, Yang, Zhang [139], see Mui [195] and Wu, Wu, Xiang [223]). If q = 0, n, then the following results are known:…”