Three circles theorems for Schrödinger operators on cylindrical ends and geometric applications

DOI10.1002/cpa.20232zbMath1170.35035arXivmath/0701302OpenAlexW2148586446MaRDI QIDQ3532829

Camillo De Lellis, Tobias Holck Colding, William P. II. Minicozzi

Publication date: 28 October 2008

Published in: Communications on Pure and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0701302

zbMATH Keywords

Schrödinger operatorscylindrical endssingular laminationsthree circles theorems

Mathematics Subject Classification ID

Elliptic equations on manifolds, general theory (58J05) Schrödinger operator, Schrödinger equation (35J10) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items

Three circles theorems for harmonic functions, Harmonic and Schrödinger functions of polynomial growth on gradient shrinking Ricci solitons, A Carleman inequality on product manifolds and applications to rigidity problems, The polynomial growth solutions to some sub-elliptic equations on the Heisenberg group, Properly embedded minimal planar domains, Width and finite extinction time of Ricci flow, Non-proper helicoid-like limits of closed minimal surfaces in 3-manifolds, The classical theory of minimal surfaces, Three-spheres theorem for \(p\)-harmonic mappings

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Bilinear eigenfunction estimates and the nonlinear Schrödinger equation on surfaces
• A unique continuation theorem for solutions of elliptic partial differential equations or inequalities of second order
• Unique continuation and absence of positive eigenvalues for Schrödinger operators. (With an appendix by E. M. Stein)
• New applications of mapping degrees to minimal surface theory
• Sur le spectre des opérateurs elliptiques à bicaracteristiques toutes périodiques
• Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. I: Schrödinger equations
• Harmonic functions on manifolds
• Harmonic functions with polynomial growth
• A remark on unique continuation
• Singular limit laminations, Morse index, and positive scalar curvature
• The space of embedded minimal surfaces of fixed genus in a 3-manifold. I: Estimates off the axis for disks
• The space of embedded minimal surfaces of fixed genus in a 3-manifold. II: Multi-valued graphs in disks
• The space of embedded minimal surfaces of fixed genus in a 3-manifold. III: Planar domains
• The space of embedded minimal surfaces of fixed genus in a 3-manifold. IV: Locally simply connected
• Exponential growth solutions of elliptic equations
• Geodesic laminations with closed ends on surfaces and Morse index; Kupka-Smale metrics
• Minimal submanifolds of low cohomogeneity
• Unique continuation for elliptic operators: A geometric-variational approach
• Differential equations on riemannian manifolds and their geometric applications
• Embedded minimal disks: Proper versus nonproper—global versus local
• Lectures on spectral theory of elliptic operators