We present some results on the local solvability of the Nirenberg problem on S2. More precisely, an L2(S2) function near 1 is the Gauss curvature of an H2(S2) metric on the round sphere S2, pointwise conformal to the standard round metric on S 2, provided its L2(S2) projection into the the space of spherical harmonics of degree 2 satisfy a matrix invertibility condition, and the ratio of the L2(S2) norms of its L 2(S2) projections into the the space of spherical harmonics of degree 1 vs the space of spherical harmonics of degrees other than 1 is sufficiently small.
All Science Journal Classification (ASJC) codes
- Discrete Mathematics and Combinatorics
- Applied Mathematics
- Local solvability
- Nirenberg problem
- Prescribing Gaussian curvature