Global and local upper bounds hold for Hessians of positive heat solutions on Kähler manifolds with bisec ≥ −K, and on Riemannian manifolds with only sec ≥ −K1 plus a bound on |∇Ric|.
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Upper Bounds for Hessian Matrices of Positive Solutions to Heat Equations on K\"ahler Manifolds
Global and local upper bounds hold for Hessians of positive heat solutions on Kähler manifolds with bisec ≥ −K, and on Riemannian manifolds with only sec ≥ −K1 plus a bound on |∇Ric|.