arXiv research

New contractible domains on half-sphere with constant boundary Laplacian eigenfunctions.

Research shows conditional existence of foliations by CMC and Willmore type half-spheres near a boundary point.

Study on half spheres solves Nirenberg problem with complex blow-up analysis.

This paper is devoted to the problem of prescribing the scalar curvature under zero boundary conditions. Using dynamical and topological methods involving the study of critical points at infinity of the associated variational problem, we prove some existence results on the standard half sphere.

The paper solves a Nirenberg problem on half spheres, finding multiple blow-ups.

In this paper, we consider the problem of prescribing the scalar curvature under minimal boundary conditions on the standard four dimensional half sphere. We provide an Euler-Hopf type criterion for a given function to be a scalar curvature to a metric conformal to the standard one. Our proof involves the study of crit…

The paper solves the Nirenberg problem on high-dimensional half spheres with pinching conditions.

Small bubbles sliding on a boundary maintain half-spherical shape.

In this paper, we prove the Hijazi inequality on compact Riemannian spin manifolds under two boundary conditions: the condition associated with a chirality operator and the Riemannian version of the $\MIT$ bag condition. We then show that the limiting-case is characterized as being a half-sphere for the first condition…

The paper studies Pansu spheres in a sub-Riemannian 3-sphere and their area-minimizing properties.

The paper establishes inequalities for $p$-capacitary functions in flat half-spaces.

We consider the mean curvature flow of compact convex surfaces in Euclidean $3$-space with free boundary lying on an arbitrary convex barrier surface with bounded geometry. When the initial surface is sufficiently convex, depending only on the geometry of the barrier, the flow contracts the surface to a point in finite…

We show that a smooth radially symmetric solution $u$ to the graphic Willmore surface equation is either a constant or the defining function of a half sphere in ${\mathbb R}^3$. In particular, radially symmetric entire Willmore graphs in ${\mathbb R}^3$ must be flat. When $u$ is a smooth radial solution over a puncture…