Integral Formulas for Differential Forms on Weighted Manifolds and Applications

Key Points

A Reilly formula for differential forms was derived on weighted manifolds with nonempty boundary, offering new insights.
Key findings include extending eigenvalue estimates and proving a Poincaré-type inequality within this framework.
Analysis included weighted versions of boundary value problems, showing potential applications in various mathematical fields.
Findings may enable better understanding of differential structures in complex geometries, enhancing theoretical models.

Abstract

In this paper, we derive a Reilly formula for differential forms on weighted manifolds with nonempty boundary. As an application of this formula, we prove a Poincaré-type inequality in the same context and explore several of its consequences. We also present weighted versions of some boundary value problems and obtain new eigenvalue estimates that extend previously known results.

Integral Formulas for Differential Forms on Weighted Manifolds and Applications

Key Points

Abstract

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