Related papers: A stereological version of the Gauss-Bonnet formul…
In this work the evolution of a fluid droplet in vacuum is considered. This means that the surface tension and the fluid forces are in equilibrium at the free boundary. The fluid is governed by the incompressible quasi-steady Stokes…
We derive nonlinear stability results for numerical integrators on Riemannian manifolds, by imposing conditions on the ODE vector field and the step size that makes the numerical solution non-expansive whenever the exact solution is…
The first-order Euler-Maclaurin formula relates the sum of the values of a smooth function on an interval of integers with its integral on the same interval on $\mathbb R$. We formulate here the analogue for functions that are just of…
In this paper, we consider a class of plane curves called log-aesthetic curves and their generalization which are used in computer aided geometric design. We consider these curves in the framework of the similarity geometry and characterize…
We study necessary conditions on the geometry and the topology of domains in $\mathbb{R}^2$ that support a positive solution to a classical overdetermined elliptic problem. The ideas and tools we use come from constant mean curvature…
Weingarten surfaces are those whose principal curvatures satisfy a functional relation, whose set of solutions is called the curvature diagram or the W-diagram of the surface. Making use of the notion of geometric linear momentum of a plane…
We introduce and analyze a nonlocal generalization of Whittle--Mat\'ern Gaussian fields in which the smoothness parameter varies in space through the fractional order, $s=s(x)\in[\underline{s}\,,\bar{s}]\subset(0,1)$. The model is defined…
This paper presents a Meyer-Vietoris type gluing formula for a conformal invariant of a Riemannian surface with boundary that is defined by the determinant of the Dirichlet-to-Neumann operator. The formula is used to bound the asymptotics…
In this paper, we study the Brezis-Nirenberg problem on bounded smooth domains of R3. Using the algebraic topological argument of Bahri-Coron[2] as implemented in [6] combined with the Brendle[4]- Schoen[8]'s bubble construction, we solve…
In this article, we establish the mathematical foundations for modeling the randomness of shapes and conducting statistical inference on shapes using the smooth Euler characteristic transform. Based on these foundations, we propose two…
The equations of a planar elastica under pressure can be rewritten in a useful form by parametrising the variables in terms of the local orientation angle, $\theta$, instead of the arc length. This ``$\theta$-formulation'' lends itself to a…
In this paper, we study the 2D free boundary incompressible Euler equations with surface tension, where the fluid domain is periodic in $x_1$, and has finite depth. We construct initial data with a flat free boundary and arbitrarily small…
A simple procedure is developed to determine orbital elements of an object orbiting in a central force field which contribute more than three independent celestial positions. By manipulation of formal three point Gauss method of orbit…
We study the evolution of a self interacting scalar field in Einstein-Gauss-Bonnet theory in four dimension where the scalar field couples non minimally with the Gauss-Bonnet term. Considering a polynomial coupling of the scalar field with…
We consider the problem of prescribing the Gaussian and the geodesic curvatures of a compact surface with boundary by a conformal deformation of the metric. We derive some existence results using a variational approach, either by…
The classical Euler's problem on optimal configurations of elastic rod in the plane with fixed endpoints and tangents at the endpoints is considered. The global structure of the exponential mapping that parameterises extremal trajectories…
This note studies the behavior of Euler characteristics and of intersection homology Euler characterstics under proper morphisms of algebraic (or analytic) varieties. The methods also yield, for algebraic (or analytic) varieties, formulae…
We derive the Chern-Gauss-Bonnet Theorem for manifolds with smooth non-degenerate boundary in the pseudo-Riemannian context from the corresponding result in the Riemannian setting by examining the Euler-Lagrange equations associated to the…
In this paper, we compute sub-Riemannian limits of Gaussian curvature for a Euclidean $C^2$-smooth surface in the affine group and the group of rigid motions of the Minkowski plane away from characteristic points and signed geodesic…
In a smooth bounded domain we obtain existence, uniqueness, regularity and boundary behavior for a class of singular quasi-linear elliptic equations.