Estimates for the covariant derivative of the heat semigroup on differential forms, and covariant Riesz transforms

2021/07/01 by Baumgarth, Robert, Devyver, Baptiste, Güneysu, Batu · 2 citations
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2107.00311

Abstract

With Δ_j≥ 0 is the uniquely determined self-adjoint realization of the Laplace operator acting on j-forms on a geodesically complete Riemannian manifold M and ∇ the Levi-Civita covariant derivative, we prove amongst other things a Li-Yau type heat kernel bound for ∇ e ^-tΔ_j , if the curvature tensor of M and its covariant derivative are bounded, an exponentially weighted L^p bound for the heat kernel of ∇ e ^-tΔ_j , if the curvature tensor of M and its covariant derivative are bounded, that ∇ e ^-tΔ_j is bounded in L^p for all 1≤ p

Cited by

• L^p-Boundedness of the Covariant Riesz Transform on Differential Forms for p>2
• Estimates of heat kernels and Sobolev-type inequalities for twisted differential forms on compact Kähler manifolds

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