Related papers: The Hasse Principle for Geometric Variational Prob…
A functional for joint variational object segmentation and shape matching is developed. The formulation is based on optimal transport w.r.t. geometric distance and local feature similarity. Geometric invariance and modelling of…
A convergent numerical method for $\alpha$-dissipative solutions of the Hunter-Saxton equation is derived. The method is based on applying a tailor-made projection operator to the initial data, and then solving exactly using the generalized…
Homology-based invariants can be used to characterize the geometry of datasets and thereby gain some understanding of the processes generating those datasets. In this work we investigate how the geometry of a dataset changes when it is…
The principle of balanced holography, introduced in [1], posits that black hole information is stored in non-local correlations between the interior and exterior. Based on this concept, we propose that black hole information decomposes into…
The inhomogeneous Groshev type theory for dual Diophantine approximation on manifolds is developed. In particular, the notion of nice manifolds is introduced and the divergence part of the theory is established for all such manifolds. Our…
We prove convergence rates of linear sampling recovery of functions in abstract Bochner spaces satisfying weighted summability of their generalized polynomial chaos expansion coefficients. The underlying algorithm is a function-valued…
Some optimization problems coming from the Differential Geometry, as for example, the minimal submanifolds problem and the harmonic maps problem are solved here via interior solutions of appropriate multitime optimal control problems.…
Hasse constants and their basic properties are introduced to facilitate the connection between the lattice of subalgebras of an algebra $C$ and the natural action of the automorphism group $Aut(C)$ on $C$. These constants are then used to…
We prove that all mod $p$ Hilbert modular forms arise via multiplication by generalized partial Hasse invariants from forms whose weight falls within a certain minimal cone. This answers a question posed by Andreatta and Goren, and…
We consider the problem of minimising an inhomogeneous anisotropic elliptic functional in a class of closed $m$ dimensional subsets of $\mathbf{R}^n$ which is stable under taking smooth deformations homotopic to the identity and under local…
We investigate the geometry and topology of submanifolds under a sharp pinching condition involving extrinsic invariants like the mean curvature and the length of the second fundamental form. Several homology vanishing results are given.…
Inference of topological and geometric attributes of a hidden manifold from its point data is a fundamental problem arising in many scientific studies and engineering applications. In this paper we present an algorithm to compute a set of…
We study slowly rotating black hole solutions within Degenerate Higher Order Scalar Tensor (DHOST) theories. Starting from a static, spherically symmetric metric solution of a DHOST theory, we employ the Hartle-Thorne ansatz to model a…
We show that min-max minimal hypersurfaces can be localized. As a consequence, we obtain the sharp generalization to complete manifolds of the famous Almgren-Pitts min-max theorem in closed manifolds. We use this result to prove the…
We propose a new model-order reduction framework to poorly reducible problems arising from parametric partial differential equations with geometric variability. In such problems, the solution manifold exhibits a slowly decaying Kolmogorov…
The geometric theory of additive separation of variables is applied to the search for multiplicative separated solutions of the bi-Helmholtz equation. It is shown that the equation does not admit regular separation in any coordinate system…
An approach is proposed for recovering affine correspondences (ACs) from orientation- and scale-invariant, e.g. SIFT, features. The method calculates the affine parameters consistent with a pre-estimated epipolar geometry from the point…
A rapid algorithm is derived for the Helmholtz--Hodge decomposition on the surface of the sphere in spherical coordinates. The algorithm uncouples modes of spherical harmonics with different absolute order, writes the conversion as…
We investigate the existence of invariantly defined quasi-local hypersurfaces in the Kastor-Traschen solution containing $N$ charge-equal-to-mass black holes. These hypersurfaces are characterized by the vanishing of particular curvature…
As datasets used in scientific applications become more complex, studying the geometry and topology of data has become an increasingly prevalent part of the data analysis process. This can be seen for example with the growing interest in…