Topological obstructions to admissibility in -Loewner--Nirenberg problem
problem Admissibility condition for -Loewner--Nirenberg problem
method Exhibit topological obstructions
result Illustrate with examples
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21 results for “Loewner--Nirenberg”
Solves Loewner-Nirenberg problem on Riemannian manifolds for k ≤ n/2.
problem Solving the Loewner-Nirenberg problem on Riemannian manifolds for k ≤ n/2.
method Analyzes fully nonlinear Loewner-Nirenberg problem and uses conformal metrics.
result Solves the -Loewner-Nirenberg problem for all k ≤ n/2.
Flow approach solves Ricci equation boundary problem.
problem Solving generalized Loewner-Nirenberg problem for -Ricci equation.
method Flow approach to prove existence and uniqueness of solution.
result Solution converges to the boundary value as time goes to infinity.
Proves existence of smooth metrics with specific curvature properties.
problem Existence of smooth metrics with prescribed negative Ricci curvature.
method Formulated and proved for general domains in Euclidean space.
result Existence of smooth complete conformal metrics with prescribed negative Ricci curvature.
Two flow methods solve a problem on Riemannian manifolds, proving convergence to the Loewner-Nirenberg solution.
problem Solving the Loewner-Nirenberg problem on compact Riemannian manifolds with boundary.
method Direct flow and Yamabe flow approaches.
result Convergence of the flows to the solution of the Loewner-Nirenberg problem under various conditions.
Solutions to the -Loewner-Nirenberg problem on annuli are locally Lipschitz and not differentiablemath.AP
Solutions to a specific problem are shown to be locally Lipschitz but not differentiable.
problem Locally Lipschitz viscosity solutions to the -Loewner-Nirenberg problem on annuli.
method Analytical proof of regularity and non-differentiability.
result Solutions are $C^{1, rac{1}{k}}_{
m loc}$ in each of the annulus regions and have a jump in radial derivative.
The paper proves existence of solutions to a Loewner-Nirenberg problem on Riemannian manifolds.
problem Existence of solutions to a specific nonlinear problem on Riemannian manifolds.
method Proves existence of viscosity solutions using approximating cones and limit of smooth solutions.
result Existence of a Lipschitz viscosity solution to the Loewner-Nirenberg problem.
Solves geometric problems using fully nonlinear equations and Morse theory.
problem Geometric problems, specifically Loewner-Nirenberg and Yamabe problems.
method Investigates structure of fully nonlinear equations and applies Morse theory techniques.
result Constructs admissible metrics under weak conditions and demonstrates topological obstructions.
Maximal solution of a PDE shows boundary smoothness for certain domains.
problem Boundary behavior of solutions to a specific PDE.
method Reduction to a nonlinear Fuchsian elliptic PDE.
result Hyperbolic radius is smooth up to the boundary.
The partial uniform ellipticity and prescribed problems on the conformal classes of complete metricsmath.DG
Solves nonlinear problems on metric structures through eigenvalue counting.
problem Nonlinear equations on metric structures
method Counting large eigenvalues of linearized operators
result Solves fully nonlinear Loewner-Nirenberg and Yamabe problems
The paper examines the smoothness of solutions to a specific partial differential equation on smooth domains.
problem Regularity of viscosity solutions of the -Loewner-Nirenberg problem.
method Analysis of the Schouten tensor and geometric measure theory.
result The first derivatives of $d^{ rac{n-2}{2}} u$ are Hölder continuous in a specific region, and is smooth in another region.
The paper classifies solutions to a specific equation and finds counterexamples to boundary estimates.
problem Solutions to a conformally invariant equation of the form in the upper half-space.
method Novel application of the method of moving spheres with new estimates and regularity near the boundary.
result When , solutions form a one-parameter family, including the hyperbolic solution.
This paper carries out a renormalization of the volume of the Loewner-Nirenberg singular Yamabe metric in a given conformal class on a compact manifold-with-boundary. This generalizes the usual volume renormalization for Poincare-Einstein metrics. The coefficient of the log term in the volume expansion defines a confor…
We develop a new approach to the conformal geometry of embedded hypersurfaces by treating them as conformal infinities of conformally compact manifolds. This involves the Loewner--Nirenberg-type problem of finding on the interior a metric that is both conformally compact and of constant scalar curvature. Our first resu…
We consider the problem of finding on a given Euclidean domain of dimension a complete conformally flat metric whose Schouten curvature satisfies some equation of the form . This generalizes a problem considered by Loewner and Nirenberg for the scalar curvature. We prove the existence a…
Study on metrics on manifolds with specific curvature properties.
problem Existence of conformal metrics with negative constant scalar curvature and negative constant mean curvature.
method Construction of metrics on smooth manifolds with solid cones removed, proving existence under certain conditions.
result Existence of such metrics if and only if the dimension condition d>(n-2)/2.
Properties of hypersurface singular sets of solutions to the -Yamabe equation in the negative conemath.AP
Study properties of solutions with singularities in the negative cone.
problem Properties of solutions with singularities in the negative cone.
method Proved PDE for trace and normal derivatives, showed hypersurface is minimal for k=2.
result Hypersurface is minimal for k=2 and satisfies certain PDE.
We derive a formula of Chern-Gauss-Bonnet type for the Euler characteristic of a four dimensional manifold-with-boundary in terms of the geometry of the Loewner-Nirenberg singular Yamabe metric in a prescribed conformal class. The formula involves the renormalized volume and a boundary integral. It is shown that if the…
The negative case of the Singular Yamabe Problem concerns the existence and behavior of complete metrics with constant negative scalar curvature on the complement of a closed set in a compact Riemannian manifold which are conformally equivalent to a smooth metric on this compact manifold. When the closed set is a smoot…
The paper proves Ricci flow convergence on compact manifolds with boundary.
problem Analyzing Ricci flow on compact manifolds with boundary conditions.
method Normalized Ricci flow with prescribed mean curvature on boundary.
result The solution converges to a complete hyperbolic metric with sectional curvature < -1.
The paper extends a Ricci flow result for compact manifolds with boundary.
problem Analyzing Ricci flow on compact manifolds with boundary.
method Normalized Ricci flow with specific boundary conditions.
result The flow converges to a complete hyperbolic metric as .