## 2-Dimensional Lp-Minkowski problem

- Date: 10/02/2007

Lecturer(s):

Meiyue Jiang (Peking University)

Location:

University of British Columbia

Topic:

et S^{n-1}subset R^n be the unit sphere. The L_p-Minkowski problem

proposed by Lukwak is a natural generalization of the classical

Minkowski problem. Analytically, it is equivalent to find positive

solutions of the equation

det(

abla_{ij}u+e_{ij}u)=g(x)u^{p-1}, xin S^{n-1}, (1)

where g is a function on S^{n-1}, pin f R, e_{ij} is the standard

Riemannian metric. In this talk we will present some existence results

for the case n=2, that is, 2pi and positive solutions of the equation

''u+u=g(x)u^{p-1}, xin S1 (2)

based on variational method. Some generalizations of equation (2) will also be discussed.

Other Information:

DG-MP-PDE Seminar 2007