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In this extended abstract, we present recent results on local and global gradient estimates of different geometric types for positive solutions to a nonlinear parabolic equation on a smooth metric measure space whose underlying metric and potential evolve in time. We present some applications, including parabolic Harnack inequalities and Liouville-type theorems and discuss some related examples.

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Geometric Estimates on a Nonlinear Parabolic Equation Under Perelman-Ricci Super Flow with Applications to Global and Ancient Solutions

  • 会议论文

  • 发表日期：

    2025年

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  • Vahideh Vahidifar

摘要

In this extended abstract, we present recent results on local and global gradient estimates of different geometric types for positive solutions to a nonlinear parabolic equation on a smooth metric measure space whose underlying metric and potential evolve in time. We present some applications, including parabolic Harnack inequalities and Liouville-type theorems and discuss some related examples.