arXiv subjects

Oliver C. Schnuerer

Publications and source records attributed to Oliver C. Schnuerer.

5 recordsLinked to original sources

arXiv2003

Regularity and splitting of directed minimal cones

We show that directed minimal cones in (n+1)-dimensional Euclidean space which have at most one singularity are - besides the trivial cases: empty set, whole space - half spaces. Using blow-up techniques, this result can be used to get C^{1,lambda}-regularity for the measure-theoretic boundary of almost minimal Caccioppoli sets which are representable as subgraphs in R^n, n<=8. This provides a different method to obtain a result due to De Giorgi. We also prove a splitting theorem for general directed minimal cones. Such a cone is the Cartesian product of R^k and C, where C is an undirected minimal cone or a half-line.

math.AP↗

arXiv2003

Stability of gradient Kaehler-Ricci solitons

We study stability of non-compact gradient Kaehler-Ricci flow solitons with positive holomorphic bisectional curvature. Our main result is that any compactly supported perturbation and appropriately decaying perturbations of the Kaehler potential of the soliton will converge to the original soliton under Kaehler-Ricci flow as time tends to infinity. To obtain this result, we construct appropriate barriers and introduce an L^p-norm that decays for these barriers with non-negative Ricci curvature.

math.DG↗

arXiv2003

Schouten tensor equations in conformal geometry with prescribed boundary metric

On a manifold with boundary, we deform the metric conformally. This induces a deformation of the Schouten tensor. We fix the metric at the boundary and realize a prescribed value for the product of the eigenvalues of the Schouten tensor in the interior, provided that there exists a subsolution.

math.AP↗

arXiv2003

Translating solutions for Gauss curvature flows with Neumann boundary conditions

We consider strictly convex hypersurfaces which are evolving by the non-parametric logarithmic Gauss curvature flow subject to a Neumann boundary condition. Solutions are shown to converge smoothly to hypersurfaces moving by translation. In particular, for bounded domains we prove that convex functions with prescribed normal derivative satisfy a uniform oscillation estimate.

math.AP↗

arXiv2001

Hypersurfaces of Prescribed Gauss Curvature in Exterior Domains

We prove an existence theorem for convex hypersurfaces of prescribed Gauss curvature in the complement of a compact set in Euclidean space which are close to a cone.

math.DG↗