Related papers: The Abresch-Rosenberg Shape Operator and applicati…

Let $M$ be a closed orientable hypersurface of dimension $n$, with nonwhere vanishing mean curvature $H$, immersed into a Riemannian Spin$^c$ manifold $\mathcal Z$ carrying a parallel spinor field. The first eigenvalue…

This paper examines minimal hypersurfaces in sub-Riemannian Heisenberg groups. We extend the celebrated Simons formula and Kato inequality to the sub-Riemannian setting, and we apply them to obtain integral curvature estimates for stable…

We prove a version of the strong half-space theorem between the classes of recurrent minimal surfaces and complete minimal surfaces with bounded curvature of $\mathbb{R}^{3}_{\raisepunct{.}}$ We also show that any minimal hypersurface…

In this paper we deduce a formula for the fractional Laplace operator $(-\Delta)^{s}$ on radially symmetric functions useful for some applications. We give a criterion of subharmonicity associated with $(-\Delta)^{s}$, and apply it to a…

We study the categorification of collapsed Riemann surfaces with quadratic differentials allowing arbitrary order zeros and poles via the Verdier quotient. We establish an isomorphism between the exchange graph of hearts in the quotient…

We prove that every complete connected immersed surface with positive extrinsic curvature $K$ in $H^2\times R$ must be properly embedded, homeomorphic to a sphere or a plane and, in the latter case, study the behavior of the end. Then, we…

In this paper we study the vertex operator algebra $\mathscr D^{\text{ch}}(\mathbb H,\Gamma)$ constructed from the fixed points of the chiral differential operators on the upper half plane which is holomorphic at all the cusps, under the…

Conserved charges in theories with gauge symmetries are supported on codimension-2 surfaces in the bulk spacetime. It has recently been suggested that various classical formulations of gravity dynamics display different symmetries, and…

Let $CH$ be the class of compacta (i.e., compact Hausdorff spaces), with $BS$ the subclass of Boolean spaces. For each ordinal $alpha$ and pair $(K,L)$ of subclasses of $CH$, we define $Lev_{>=alpha}(K,L)$, the class of maps of level at…

Let R be a polynomial ring in r variables and D a dual ring upon which R acts as partial differential operators (classical apolarity). For a type two graded level Artinian algebras A=R/I, of socle degree j we consider the family of Artinian…

Using connections to random matrix theory and orthogonal polynomials, we develop a framework for obtaining explicit closed-form formulae for the number, $\mathscr{N}_{g}(2\nu,j)$, of connected $2\nu$-valent labeled graphs with $j$ vertices…

Let $ S $ be a hyperbolic surface. We investigate the topology of the space of all curves on $ S $ which start and end at given points in given directions, and whose curvatures are constrained to lie in a given interval $…

We provide a congruence theorem for minimal surfaces in $S^5$ with constant contact angle using Gauss-Codazzi-Ricci equations. More precisely, we prove that Gauss-Codazzi-Ricci equations for minimal surfaces in $S^5$ with constant contact…

We study almost complex surfaces in the nearly K\"ahler $S^3\times S^3$. We show that there is a local correspondence between almost complex surfaces and solutions of the H-surface equation introduced by Wente. We find a global holomorphic…

We consider a smooth, compact and embedded hypersurface $\Sigma$ without boundary and show that the corresponding (shifted) surface Stokes operator $\omega+A_{S,\Sigma}$ admits a bounded $H^\infty$-calculus with angle smaller than $\pi/2$,…

We investigate ortho-integral (OI) hyperbolic surfaces with totally geodesic boundaries, defined by the property that every orthogeodesic (i.e. a geodesic arc meeting the boundary perpendicularly at both endpoints) has an integer…

In this article, we continue the study of the problem of $L^p$-boundedness of the maximal operator $M$ associated to averages along isotropic dilates of a given, smooth hypersurface $S$ of finite type in 3-dimensional Euclidean space. An…

Let $H\subset \R^{d+1}$ be a compact, convex, analytic hypersurface of finite type with a smooth measure $\sigma $ on $H$. Let $\kappa$ denote the Gaussian curvature on $H$. We consider the oscillatory integral $(\kappa^{1/2}…

Starting out from a new description of a class of parameter-dependent pseudodifferential operators with finite regularity number due to G. Grubb, we introduce a calculus of parameter-dependent, poly-homogeneous symbols whose homogeneous…

This paper introduces a set of numerical methods for Riemannian shape analysis of 3D surfaces within the setting of invariant (elastic) second-order Sobolev metrics. More specifically, we address the computation of geodesics and geodesic…