紀要論文

紀要論文

text

Osaka Journal of Mathematics. 2025, 62(1), p. 1-17

SPECTRUM AND PARABOLIC HEAT KERNEL ON SMOOTH COMPACT METRIC MEASURE SPACES

Osaka University and Osaka City University, Departments of Mathematics

英語

text

2025-01

In this paper, by utilizing some functional inequalities and combining with De Giorgi-Moser iteration technique, we obtain some estimates for the weighted L^∞-norm of eigenfunctions of the Witten-Laplacian on smooth metric measure spaces, which enables us to establish the upper bounds for multiplicity of corresponding eigenvalues. We remark that those estimates are established without any assumption on curvature. As an important application, we prove the uniform convergence of the heat kernel of weighted parabolic equation on smooth metric measure spaces. In addition, our result remains ture for some isomorphism classes of weighted Riemannian manifold with boundary satisfying certain conditions. Furthermore, by the standard theory of elliptic and parabolic equations, we prove the regularity and uniqueness of parabolic heat kernel on smooth metric measure spaces.

10.18910/100442

100442

SPECTRUM AND PARABOLIC HEAT KERNEL ON SMOOTH COMPACT METRIC MEASURE SPACES

Osaka University and Osaka City University, Departments of Mathematics

英語

2025-01

Osaka Journal of Mathematics

62

1

1

17

https://hdl.handle.net/11094/100442

10.18910/100442

https://doi.org/10.18910/100442