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Local Hessian estimates of solutions to nonlinear parabolic equations along Ricci flow. (English) Zbl 1523.58029

The authors analyze positive solutions to the nonlinear parabolic equation involving Laplace-Beltrami operator and power-like external force term. The evolution of a scalar quantity is investigated on a time-dependent Riemannian manifold with a fixed metric. The curvature estimates imply Harnack type inequalities.

MSC:

58J35 Heat and other parabolic equation methods for PDEs on manifolds
35K05 Heat equation
53C21 Methods of global Riemannian geometry, including PDE methods; curvature restrictions
58E20 Harmonic maps, etc.
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