Stability of complex hyperbolic space under curvature-normalized Ricci flow

作者：Wu Haotian^*

来源：Geometriae Dedicata, 2013, 164(1): 231-258.

DOI：10.1007/s10711-012-9770-9

• Stability
• Ricci flow
• Complex hyperbolic space
• Maximal regularity
• Interpolation spaces

Using the maximal regularity theory for quasilinear parabolic systems, we prove two stability results of complex hyperbolic space under the curvature-normalized Ricci flow in complex dimensions two and higher. The first result is on a closed manifold. The second result is on a complete noncompact manifold. To prove both results, we fully analyze the structure of the Lichnerowicz Laplacian on complex hyperbolic space. To prove the second result, we also define suitably weighted little Holder spaces on a complete noncompact manifold and establish their interpolation properties.

• 出版日期2013-6