Abstract
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In this talk, we shall first obtain a constant rank theorem for the second fundamental form of the convexity spacetime level sets for the standard parabolic PDE. Then we use the deformation process to get the convexity of the spacetime level sets for a class initial boundary value problem for parabolic PDE, under the assumption that the initial data is subharmonic and its level sets is convexity. This is ajoint work with Chen Chuanqiang (USTC) and P.Salani (Firenze).
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