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On the microscopic spacetime convexity principle of fully nonlinear parabolic equations I: Spacetime convex solutions

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  • Spacetime convexity is a basic geometric property of the solutions of parabolic equations. In this paper, we study microscopic convexity properties of spacetime convex solutions of fully nonlinear parabolic partial differential equations and give a new simple proof of the constant rank theorem in [11].
    Mathematics Subject Classification: Primary: 35K10; Secondary: 35B99.


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