Eigenvalue asymptotics for weighted Laplace equations on rough Riemannian manifolds with boundary

DOI10.2422/2036-2145.201902_003zbMath1483.58006arXiv1811.08217OpenAlexW3129182414WikidataQ115228251 ScholiaQ115228251MaRDI QIDQ5037196

Lashi Bandara, Medet Nursultanov, Julie Rowlett

Publication date: 28 February 2022

Published in: ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1811.08217

zbMATH Keywords

eigenvalue asymptoticsrough Riemannian manifoldweighted Laplace equations

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds (58B20)

Related Items

On instability mechanisms for inverse problems, Narrow escape problem in the presence of the force field

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The Kato square root problem on vector bundles with generalised bounded geometry
• Rough metrics on manifolds and quadratic estimates
• 100 years of Weyl's law
• Continuity of solutions to space-varying pointwise linear elliptic equations
• Spectral geometry of singular Riemannian spaces
• Uniformly elliptic operators on Riemannian manifolds
• Quadratic estimates and functional calculi of perturbed Dirac operators
• Asymptotic expansion of the hypoelliptic heat kernel on the diagonal
• Isospectral plane domains and surfaces via Riemannian orbifolds
• A selection-migration model in population genetics
• Zeta function regularization of path integrals in curved spacetime
• On the structure of spaces with Ricci curvature bounded below. I
• Heat kernel asymptotics and the distance function in Lipschitz Riemannian manifolds
• On the structure of spaces with Ricci curvature bounded below. II
• On the structure of spaces with Ricci curvature bounded below. III
• Short-time behavior of the heat kernel and Weyl's law on \(\mathrm{RCD}^*(K,N)\) spaces
• Spectral asymptotics for sub-Riemannian Laplacians. I: Quantum ergodicity and quantum limits in the 3-dimensional contact case
• Deformation of \(C^0\) Riemannian metrics in the direction of their Ricci curvature
• The solution of the Kato square root problem for second order elliptic operators on \(\mathbb R^n\).
• Heat kernels and Green's functions on limit spaces
• Weyl's law on \(RCD^{\ast} (K, N)\) metric measure spaces
• Length structures on manifolds with continuous Riemannian metrics
• A flow tangent to the Ricci flow via heat kernels and mass transport
• A manifold which does not admit any differentiable structure
• Rand- und Eigenwertaufgaben in Sobolewschen Räumen
• Curvature and the eigenvalues of the Laplacian
• One can hear the corners of a drum
• The Sound of Symmetry
• The Kato square root problem on submanifolds
• Principal Eigenvalues for Problems with Indefinite Weight Function on R N
• On Principal Eigenvalues for Indefinite Problems in Euclidean Space
• On some linear and nonlinear eigenvalue problems with an indefinite weight function
• Développement asymptotique de la densité d’une diffusion dégénérée
• Principal Eigenvalues for Indefinite-Weight Elliptic Problems in R n
• The existence of principal eigenvalues for problems with indefinite weight function on ℝ^k
• Nonsmooth differential geometry– An approach tailored for spaces with Ricci curvature bounded from below
• Geometric singularities and a flow tangent to the Ricci flow
• THE KATO SQUARE ROOT PROBLEM FOR MIXED BOUNDARY VALUE PROBLEMS
• Can One Hear the Shape of a Drum?
• A simple triangulation method for smooth manifolds
• On the Comparability of A 1/2 and A ∗ 1/2