Abstract
On a complete non-compact gradient shrinking Ricci soliton, we prove the analyticity in time for smooth solutions of the heat equation with quadratic exponential growth in the space variable. This growth condition is sharp. As an application, we give a necessary and sufficient condition on the solvability of the backward heat equation in a class of functions with quadratic exponential growth on shrinkers.
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The author sincerely thanks Professor Qi S. Zhang for helpful discussion about the work [3].
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This work was partially supported by the National Natural Science Foundation of China (11671141) and the Natural Science Foundation of Shanghai (17ZR1412800).
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Wu, J. Time Analyticity for the Heat Equation on Gradient Shrinking Ricci Solitons. Acta Math Sci 42, 1690–1700 (2022). https://doi.org/10.1007/s10473-022-0424-1
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DOI: https://doi.org/10.1007/s10473-022-0424-1