Fourth-order problem on half-ball with corner behavior.
problem Fourth-order problem with corner behavior on half-ball.
method Conformal mapping to isolate corner effect.
result Gauss-Bonnet formula simplifies to constant term at corner.
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11 results for “half-ball”
Paper proves inequality for capillary hypersurfaces with new proof.
problem Proving a Heintze-Karcher type inequality for hypersurfaces with capillary boundary.
method Using a mixed boundary value problem in Reilly type formula to establish the inequality.
result New proof of Alexandrov type theorem for capillary hypersurfaces.
Some Properties of the Intersection of Free Boundary Minimal Hypersurfaces in Euclidean Ballsmath.DG
Two minimal hypersurfaces in a ball intersect in any half-ball.
problem Intersection properties of minimal hypersurfaces in a ball.
method Analyzing the intersection of two minimal hypersurfaces in a unit Euclidean ball.
result Intersection point in any half-ball, strong Frankel property.
The critical catenoid is uniquely determined by certain symmetries of its boundary.
problem Uniqueness of free boundary minimal annuli in a half-ball.
method Symmetry analysis and boundary conditions.
result An embedded free boundary minimal annulus with specific symmetries is congruent to the critical catenoid.
Existence and boundary regularity away from the corners are established for two-dimensional Monge-Ampère equations on convex polytopes with Guillemin boundary conditions. An important step is to derive an expansion in terms of functions and for solutions to equations of the form $\det D^2u(x,y) = y^{-…
We build new examples of extremal domains with small prescribed volume for the first eigenvalue of the Laplace-Beltrami operator in some Riemannian manifold with boundary. These domains are close to half balls of small radius centered at a nondegenerate critical point of the mean curvature function of the boundary of t…
We prove existence of solutions to boundary value problems and obstacle problems for degenerate-elliptic, linear, second-order partial differential operators with partial Dirichlet boundary conditions using a new version of the Perron method. The elliptic operators considered have a degeneracy along a portion of the do…
Characterizations of umbilical hypersurfaces by partially overdetermined problems in space formsmath.DG
Paper characterizes umbilical hypersurfaces using a generalized overdetermined problem.
problem Characterizing umbilical hypersurfaces in space forms.
method Using a Serrin-type partially overdetermined problem with inhomogeneous Robin boundary condition.
result Any contact angle θ ∈ (0, π) can be achieved, generalizing previous results.
Paper studies minimal surfaces in curved spaces, proving existence and properties.
problem Existence and properties of minimal surfaces with free boundaries.
method Degree theory, Banach manifold construction, Fredholm map analysis.
result Space of partially free boundary minimal half disks is a Banach manifold.
Let and be two compact Riemannian manifolds with boundary and respectively. The Escobar problem consists in prescribing a conformal metric on a compact manifold with boundary with zero scalar curvature in the interior and constant mean curvature of the boundar…
Paper proves rigidity of minimal disks in 3-balls with non-negative Ricci curvature.
problem Rigidity of free boundary minimal disks in 3-balls with non-negative Ricci curvature.
method Min-max methods and rigidity statements for half-balls with non-negative Ricci curvature.
result Existence and properties of minimal disks with least area in 3-balls.