A flow approach to the planar Lp$L_p$ Minkowski problem

Abstract

This paper will establish the asymptotic behavior of an anisotropic areapreserving flow which shows the existence of smooth solutions of the planar 𝐿 𝑝 Minkowski problem for 𝑝 ≠ 0. K E Y W O R D Sarea-preserving flow, asymptotic behavior, 𝐿 𝑝 Minkowski problemwhere ℎ 𝑖𝑗 is the covariant derivative of ℎ with respect to an orthonormal frame on 𝑆 𝑛−1 and 𝛿 𝑖𝑗 is the Kronecker delta.