Conformal upper bounds for the volume spectrum
Zhichao Wang
TL;DR
This paper establishes upper bounds on the volume spectrum of Riemannian manifolds based solely on volume, dimension, and a conformal invariant, advancing understanding of geometric spectral properties.
Contribution
It introduces conformal upper bounds for the volume spectrum that depend only on fundamental geometric quantities, providing new insights into spectral geometry.
Findings
Derived upper bounds for the volume spectrum based on conformal invariants.
Showed bounds depend only on volume, dimension, and a conformal invariant.
Enhanced understanding of the relationship between geometry and spectral properties.
Abstract
In this paper, we prove upper bounds for the volume spectrum of a Riemannian manifold that depend only on the volume, dimension and a conformal invariant.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Point processes and geometric inequalities · Numerical methods in inverse problems