Mahidol University International College
Yau’s gradient estimate is a fundamental result in partial differential equations and differential geometry. Its variants include Li-Yau gradient estimate which play a role in the proof of Poincare conjecture by Perelman in 2003. In this talk, we will derive gradient estimate for harmonic functions in Euclidean space by elementary methods. Then we will discuss about Riemannian surfaces and derive the gradient estimate for harmonic functions on a surface with negative curvature, i.e., Poincare disc.