Monotonicity formulas in potential theory
DOI10.1007/s00526-019-1665-2zbMath1428.35008arXiv1606.02489OpenAlexW2990028454WikidataQ126652290 ScholiaQ126652290MaRDI QIDQ2278106
Virginia Agostiniani, Lorenzo Mazzieri
Publication date: 9 December 2019
Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1606.02489
Boundary value problems for second-order elliptic equations (35J25) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Potentials and capacities, extremal length and related notions in higher dimensions (31B15) Symmetries, invariants, etc. in context of PDEs (35B06) Overdetermined boundary value problems for PDEs and systems of PDEs (35N25) Topological and monotonicity methods applied to PDEs (35A16)
Related Items
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Riemannian aspects of potential theory
- \(P\)-capacity vs surface-area
- Comparing monotonicity formulas for electrostatic potentials and static metrics
- On the expansion of starshaped hypersurfaces by symmetric functions of their principal curvatures
- Nodal sets for solutions of elliptic equations
- On Aleksandrov-Fenchel inequalities for \(k\)-convex domains
- The inverse mean curvature flow and \(p\)-harmonic functions
- Asymptotic behavior for singularities of the mean curvature flow
- Flow of nonconvex hypersurfaces into spheres
- On the capacity of surfaces in manifolds with nonnegative scalar curvature
- Partially overdetermined elliptic boundary value problems
- The quermassintegral inequalities for \(k\)-convex starshaped domains
- Partial regularity of the zero-set of solutions of linear and superlinear elliptic equations
- Some overdetermined boundary value problems for harmonic functions
- The inverse mean curvature flow and the Riemannian Penrose inequality
- Critical sets of solutions to elliptic equations.
- Symmetry in exterior boundary value problems for quasilinear elliptic equations via blow-up and a priori estimates
- New monotonicity formulas for Ricci curvature and applications. I
- Minkowski inequalities via nonlinear potential theory
- Sharp geometric inequalities for closed hypersurfaces in manifolds with nonnegative Ricci curvature
- On the geometry of the level sets of bounded static potentials
- Geometric aspects of \(p\)-capacitary potentials
- Inequalities for quermassintegrals on \(k\)-convex domains
- Min-max theory and the Willmore conjecture
- Ricci curvature and monotonicity for harmonic functions
- Overdetermined problems with possibly degenerate ellipticity, a geometric approach
- Symmetry for an overdetermined boundary problem in a punctured domain
- On a long-standing conjecture by Pólya-Szegö and related topics
- On the mass of static metrics with positive cosmological constant: I
- A Minkowski Inequality for Hypersurfaces in the Anti‐de Sitter‐Schwarzschild Manifold
- Some regularity theorems in riemannian geometry
- On Some Maximum Principles Involving Harmonic Functions and Their Derivatives
- Comparison results for capacity
- Monotonicity and its analytic and geometric implications
- Optimal Integral Pinching Results
- Some sphere theorems in linear potential theory
- Mass-Capacity Inequalities for Conformally Flat Manifolds with Boundary
- Critical Sets of Elliptic Equations
- On the Total Curvature of Immersed Manifolds, I: An Inequality of Fenchel-Borsuk-Willmore
- Splitting Theorems, Symmetry Results and Overdetermined Problems for Riemannian Manifolds
- On a theorem of Fenchel-Borsuk-Willmore-Chern-Lashof