East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
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EVOLUTION EQUATIONS ON A RIEMANNIAN MANIFOLD WITH A LOWER RICCI CURVATURE BOUND

  • Received : 2013.12.12
  • Accepted : 2014.01.10
  • Published : 2014.01.31
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Abstract

We consider the parabolic evolution differential equation such as heat equation and porus-medium equation on a Riemannian manifold M whose Ricci curvature is bounded below by $-(n-1)k^2$ and bounded below by 0 on some amount of M. We derive some bounds of differential quantities for a positive solution and some inequalities which resemble Harnack inequalities.

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References

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