Supercritical dual k-Minkowski flows with general prescribed data: a priori estimates and asymptotic convergence

Let k be an integer from 1 to n, let f be a positive smooth function on the unit sphere, and consider the normalized flow X_t = -f({nu})|X|^{alpha} sigma_k({kappa}) {nu} + beta X, beta = C_n^k. In the supercritical range alpha > k+1, we prove the flow exists for all time and converges exponentially