一类抛物型方程在Finsler流形上的Hamilton-Souplet-Zhang型梯度估计

IF 0.7 4区数学 Q3 MATHEMATICS

Differential Geometry and its Applications Pub Date : 2025-06-09 DOI:10.1016/j.difgeo.2025.102264

Zisu Zhao

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引用次数: 0

摘要

利用一个新的拉普拉斯比较定理，我们得到了非紧正向完全Finsler流形上一类特殊非线性抛物方程（Finslerian对数Schrödinger方程）的Souplet-Zhang型梯度估计。方程中的所有系数在流形上随时间变化。作为应用，我们得到了一个局部的Harnack不等式和一个liouville型定理。

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A Hamilton-Souplet-Zhang type gradient estimate for a class of parabolic equations on Finsler manifolds

Employing a new Laplacian comparison theorem, we have derived a Souplet-Zhang type gradient estimate for a specific nonlinear parabolic equation (Finslerian logarithmic Schrödinger equation) on a non-compact forward complete Finsler manifold with some curvatures bounded from below. All the coefficients in our equations vary with time on the manifold. As applications, we obtain a local Harnack inequality and a Liouville-type theorem.

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来源期刊

Differential Geometry and its Applications 数学-数学

CiteScore

1.00

自引率

20.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Differential Geometry and its Applications publishes original research papers and survey papers in differential geometry and in all interdisciplinary areas in mathematics which use differential geometric methods and investigate geometrical structures. The following main areas are covered: differential equations on manifolds, global analysis, Lie groups, local and global differential geometry, the calculus of variations on manifolds, topology of manifolds, and mathematical physics.