Asymptotically mean value harmonic functions in subriemannian and RCD settings

DOI10.1007/s12220-022-01132-6OpenAlexW4313890004WikidataQ126087399 ScholiaQ126087399MaRDI QIDQ2679614

Elefterios Soultanis, Tomasz Adamowicz, Antoni Kijowski

Publication date: 23 January 2023

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2301.06513

zbMATH Keywords

harmonic functionsmean value propertymetric measure spaces

Mathematics Subject Classification ID

Harmonic, subharmonic, superharmonic functions on other spaces (31C05) PDEs on Heisenberg groups, Lie groups, Carnot groups, etc. (35R03) Potential theory on fractals and metric spaces (31E05)

Related Items (1)

Asymptotically mean value harmonic functions in doubling metric measure spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Synthetic theory of Ricci curvature bounds
• Nonlinear potential theory on metric spaces
• Harmonic functions on metric measure spaces
• Harmonic functions on metric measure spaces: Convergence and compactness
• Conformality and \(Q\)-harmonicity in Carnot groups
• Constant mean curvature spheres in Riemannian manifolds
• The Dirichlet problem for sublaplacians on nilpotent Lie groups - geometric criteria for regularity
• A concentration-compactness principle for sequences of Riemannian surfaces.
• Dirichlet forms and analysis on Wiener space
• Boundary behavior of nonnegative solutions of subelliptic equations in NTA domains for Carnot-Carathéodory metrics
• Differentiability of Lipschitz functions on metric measure spaces
• The Riemannian structure of Alexandrov spaces
• Lipschitz continuity of Cheeger-harmonic functions in metric measure spaces
• DC calculus
• Newtonian spaces: An extension of Sobolev spaces to metric measure spaces
• Sobolev spaces and harmonic maps for metric space targets
• Yau's gradient estimates on Alexandrov spaces
• Quantitative gradient estimates for harmonic maps into singular spaces
• Asymptotically mean value harmonic functions in doubling metric measure spaces
• Boundary regularity and stability for spaces with Ricci bounded below
• Asymptotic mean value Laplacian in metric measure spaces
• Korevaar-Schoen's energy on strongly rectifiable spaces
• Mean value property and harmonicity on Carnot-Carathéodory groups
• Spectral stability of metric-measure Laplacians
• Mean value properties and unique continuation
• Structure theory of metric measure spaces with lower Ricci curvature bounds
• On the characterization of \(p\)-harmonic functions on the Heisenberg group by mean value properties
• Metric measure spaces with Riemannian Ricci curvature bounded from below
• On the geometry of metric measure spaces. I
• On the geometry of metric measure spaces. II
• Characterization by asymptotic mean formulas of \(q\)-harmonic functions in Carnot groups
• On the regularity of Alexandrov surfaces with curvature bounded below
• Metric-measure boundary and geodesic flow on Alexandrov spaces
• On the asymptotic mean value property for planar 𝑝-harmonic functions
• Alexandrov meets Lott--Villani--Sturm
• On the definition and properties of $p$-harmonious functions
• Sobolev spaces in metric measure spaces: reflexivity and lower semicontinuity of slope
• A Bishop-type inequality on metric measure spaces with Ricci curvature bounded below
• An Asymptotic Mean Value Characterization for a Class of Nonlinear Parabolic Equations Related to Tug-of-War Games
• A new proof of Gromov’s theorem on groups of polynomial growth
• Stratified Lie Groups and Potential Theory for their Sub-Laplacians
• Sobolev met Poincaré
• Non-collapsed spaces with Ricci curvature bounded from below
• Boundedness of averaging operators on geometrically doubling metric spaces
• SOBOLEV CLASSES AND HORIZONTAL ENERGY MINIMIZERS BETWEEN CARNOT–CARATHÉODORY SPACES
• Regularity at the boundary for solutions of nonlinear subelliptic equations
• A note on generalized Laplacians and minimal surfaces
• Constancy of the Dimension for RCD(K,N) Spaces via Regularity of Lagrangian Flows
• Improvements of upper curvature bounds
• Sobolev Spaces on Metric Measure Spaces
• Geometric Analysis
• Surface measures in Carnot-Carathéodory spaces

This page was built for publication: Asymptotically mean value harmonic functions in subriemannian and RCD settings