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Let $M$ be a topological $G_2$-manifold. We prove that the space of infinitesimal associative deformations of a compact associative submanifold $Y$ with boundary in a coassociative submanifold $X$ is the solution space of an elliptic…

In this paper, we solve the fractional anisotropic Calder\'on problem with external data in the Euclidean space, in dimensions two and higher, for smooth Riemannian metrics that agree with the Euclidean metric outside a compact set.…

In this paper we explore the connection between special degenerations of algebraic manifolds and geodesics in the space of Kahler metrics. We provide a new and general geometric construction of nontrivial solutions for the geodesic…

We introduce a class of maps from an affine flat into a Riemannian manifold that solve an elliptic system defined by the natural second order elliptic operator of the affine structure and the nonlinear Riemann geometry of the target. These…

We study holomorphic isometries between bounded symmetric domains with respect to the Bergman metrics up to a normalizing constant. In particular, we first consider a holomorphic isometry from the complex unit ball into an irreducible…

We introduce a sequence of conformally invariant scalar curvature quantities, defined along the conformal infinity of a conformally compact (CC) manifold, that measure the failure of a CC metric to have constant negative scalar curvature in…

We consider a nonlinear version of the Yamabe problem on locally conformally flat compact manifolds with boundary. The main technique we used is to derive boundary $C^2$ estimates directly from boundary $C^0$ estimates. In particular, the…

In this paper we present a unified simple approach to anisotropic Hardy inequalities in various settings. We consider Hardy inequalities which involve a Finsler distance from a point or from the boundary of a domain. The sharpness and the…

After introducing the different boundary geometries of rank one symmetric spaces, we state and prove Fried's theorem in the general setting of all those geometries: a closed manifold with a similarity structure is either complete or the…

It is well-known that the deformation problem of a compact coisotropic submanifold $C$ in a symplectic manifold is obstructed in general. We show that it becomes unobstructed if one only allows coisotropic deformations whose characteristic…

The state of art of electromagnetic integral equations has seen significant growth over the past few decades, overcoming some of the fundamental bottlenecks: computational complexity, low frequency and dense discretization breakdown,…

Among the general class of metric-affine theories of gravity, there is a special class conformed by those endowed with a projective symmetry. Perhaps the simplest manner to realise this symmetry is by constructing the action in terms of the…

In two-dimensional conformal field theory, we analyze conformally invariant boundary conditions which break part of the bulk symmetries. When the subalgebra that is preserved by the boundary conditions is the fixed algebra under the action…

We characterize the image of the Poisson transform on any distinguished boundary of a Riemannian symmetric space of the noncompact type by a system of differential equations. The system corresponds to a generator system of a two sided…

A linear connection on a Lie algebroid is called a Cartan connection if it is suitably compatible with the Lie algebroid structure. Here we show that a smooth connected manifold $M$ is locally homogeneous - i.e., admits an atlas of charts…

We obtain a comparison result for solutions to nonlinear fully anisotropic elliptic problems by means of anisotropic symmetrization. As consequence we deduce a priori estimates for norms of the relevant solutions.

Given a compact manifold with boundary with unknown Riemannian metric. The problem is to reconstruct the metric in a class of conformal metrics from knowledge of lengths of all closed geodesics (kinematic data). An integral inequality is…

We construct a first order local model for Poisson manifolds around a large class of Poisson submanifolds and we give conditions under which this model is a local normal form. The resulting linearization theorem includes as special cases…

We consider the massive Klein-Gordon field on the half line with and without a Robin boundary potential.The field is coupled at the boundary to a harmonic oscillator.We solve the system classically and observe the existence of classical…

While raw cosine similarity in pretrained embedding spaces exhibits strong rank correlation with human judgments, anisotropy induces systematic miscalibration of absolute values: scores concentrate in a narrow high-similarity band…