46 citations · 460 across the 44 of their papers we have counts for
44 papers
Capillary quermassintegral inequalities in the unit ball
Shujing Pan, Julian Scheuer
This paper is about hypersurfaces with boundary lying in the Euclidean unit ball, which meet the unit sphere at a fixed angle . Such hypersurfaces are called …
Foliation of null cones by surfaces of constant spacetime mean curvature near MOTS
Ben Lambert, Julian Scheuer
Marginally Outer Trapped Surfaces (MOTS) in spacetimes are well-known to indicate the existence of black holes. Using flow techniques, we prove that a neighbourhood of a stable MOT…
The quermassintegral inequalities for horo-convex domains in the sphere
Shujing Pan, Julian Scheuer
We study a new notion of convexity for subsets of the unit sphere, which closely resembles the horo-convexity for subsets of the hyperbolic space. We call this notion, accordingly,…
Two properties of optimisers for the reverse isoperimetric problem
Deniz M. Hamdy, Julian Scheuer
The reverse isoperimetric problem asks for existence and properties of bounded convex sets in a Riemannian manifold which maximise the perimeter under all those sets of fixed volum…
Fractional Dirichlet problems with an overdetermined nonlocal Neumann condition
Michele Gatti, Julian Scheuer, Tobias Weth
We investigate symmetry and quantitative approximate symmetry for an overdetermined problem related to the fractional torsion equation in a regular open, bounded set $Ω\subseteq \m…
Capillary Christoffel-Minkowski problem
Yingxiang Hu, Mohammad N. Ivaki, Julian Scheuer
The result of Guan and Ma (Invent. Math. 151 (2003)) states that if is spherically convex, then arises as the curvature (the -…
Stability of the Wulff shape with respect to anisotropic curvature functionals
Julian Scheuer, Xuwen Zhang
For a function which foliates a one-sided neighbourhood of a closed hypersurface , we give an estimate of the distance of to a Wulff shape in terms of the -norm o…
Stability of the quermassintegral inequalities in hyperbolic space
Prachi Sahjwani, Julian Scheuer
For the quermassintegral inequalities of horospherically convex hypersurfaces in the -dimensional hyperbolic space, where , we prove a stability estimate relating t…
A fractional Willmore-type energy functional -- subcritical observations
Simon Blatt, Giovanni Giacomin, Julian Scheuer +1
We investigate surfaces with bounded L^p-norm of the fractional mean curvature, a quantity we shall refer to as fractional Willmore-type functional. In the subcritical case and und…
A capillary problem for spacelike mean curvature flow in a cone of Minkowski space
Wilhelm Klingenberg, Ben Lambert, Julian Scheuer
Consider a convex cone in three-dimensional Minkowski space which either contains the lightcone or is contained in it. This work considers mean curvature flow of a proper spacelike…
The quermassintegral preserving mean curvature flow in the sphere
Esther Cabezas-Rivas, Julian Scheuer
We introduce a mean curvature flow with global term of convex hypersurfaces in the sphere, for which the global term can be chosen to keep any quermassintegral fixed. Then, startin…
Stability for Serrin's problem and Alexandroff's theorem in warped product manifolds
Julian Scheuer, Chao Xia
We prove quantitative versions for several results from geometric partial differential equations. Firstly, we obtain a double stability theorem for Serrin's overdetermined problem…
Mean curvature flow in null hypersurfaces and the detection of MOTS
Henri Roesch, Julian Scheuer
We study the mean curvature flow in 3-dimensional null hypersurfaces. In a spacetime a hypersurface is called null, if its induced metric is degenerate. The speed of the mean curva…
Stability from rigidity via umbilicity
Julian Scheuer
We consider a range of geometric stability problems for hypersurfaces of spaceforms. One of the key results is an estimate relating the distance to a geodesic sphere of an embedded…
A fully-nonlinear flow and quermassintegral inequalities in the sphere
Chuanqiang Chen, Pengfei Guan, Junfang Li +1
This expository paper presents the current knowledge of particular fully nonlinear curvature flows with local forcing term, so-called locally constrained curvature flows. We focus…
Constant rank theorems for curvature problems via a viscosity approach
Paul Bryan, Mohammad N. Ivaki, Julian Scheuer
An important set of theorems in geometric analysis consists of constant rank theorems for a wide variety of curvature problems. In this paper, for geometric curvature problems in c…
Minkowski inequalities and constrained inverse curvature flows in warped spaces
Julian Scheuer
This paper deals with locally constrained inverse curvature flows in a broad class of Riemannian warped spaces. For a certain class of such flows we prove long time existence and s…
Extrinsic curvature flows and applications
Julian Scheuer
These notes arose from a mini lecture series the author gave at the Early Career Researchers Workshop on Geometric Analysis and PDEs, held in January 2020 at the Matrix institute o…
Parabolic approaches to curvature equations
Paul Bryan, Mohammad N. Ivaki, Julian Scheuer
We employ curvature flows without global terms to seek strictly convex, spacelike solutions of a broad class of elliptic prescribed curvature equations in the simply connected Riem…
Concavity of solutions to degenerate elliptic equations on the sphere
Mat Langford, Julian Scheuer
We prove the concavity of classical solutions to a wide class of degenerate elliptic differential equations on strictly convex domains of the unit sphere. The proof employs a suita…
Isoperimetric problems for spacelike domains in generalized Robertson-Walker spaces
Ben Lambert, Julian Scheuer
We use a locally constrained mean curvature flow to prove the isoperimetric inequality for spacelike domains in generalized Robertson-Walker spaces satisfying the null convergence…
The Minkowski inequality in de Sitter space
Julian Scheuer
The classical Minkowski inequality in the Euclidean space provides a lower bound on the total mean curvature of a hypersurface in terms of the surface area, which is optimal on rou…
Negatively Curved Three-Manifolds, Hyperbolic Metrics, Isometric Embeddings In Minkowski Space And The Cross Curvature Flow
Paul Bryan, Mohammad N. Ivaki, Julian Scheuer
This short note is a mostly expository article examining negatively curved three-manifolds. We look at some rigidity properties related to isometric embeddings into Minkowski space…
Asymptotic estimates for the Willmore flow with small energy
Ernst Kuwert, Julian Scheuer
Kuwert and Schätzle showed in 2001 that the Willmore flow converges to a standard round sphere, if the initial energy is small. In this situation, we prove stability estimates for…