arXiv subjects

Samuel Bronstein

Publications and source records attributed to Samuel Bronstein.

10 recordsLinked to original sources

arXiv2025

Dominating manifolds by radial spaces

This paper is devoted to a kind of rearrangement of functions on CD(k,n)-spaces, which satisfy a Polya-Szeg\"o type inequality. We use this rearrangement to prove the validity of a Moser-Trudinger type inequality on a wide class of metric measure spaces satisfying a CD(k,n)-curvature-dimension inequality. As a consequence, we give a characterization, among manifolds with lower bounded Ricci curvature, of those admitting a Moser-Trudinger type inequality.

math.DG↗

arXiv2025

Anosov deformations of Barbot representations

We construct for each conformal structure on a closed orientable surface of genus at least 2 a proper slice in the character variety of representations of the associated surface group into SL(3,R) that belongs to the Barbot component and show that the corresponding representations are Borel Anosov. We describe a fibered geometric structure in the space of full flags associated with these representations.

math.GT↗

arXiv2024

Almost-Fuchsian representations in PU(2,1)

In this paper, we study nonmaximal representations of surface groups in PU(2,1). In genus large enough, we show the existence of convex-cocompact representations of non-maximal Toledo invariant admitting a unique equivariant minimal surface, which is holomorphic and almost totally geodesic. These examples can be obtained for any Toledo invariant of the form 2-2g +2/3 d, provided g is large compared to d. When d is not divisible by 3, this yields examples of convex-cocompact representations in PU(2,1) which do not lift to SU(2,1)

math.DG↗

arXiv2024

Tykhyy's Conjecture on finite mapping class group orbits

We classify the finite orbits of the mapping class group action on the character variety of Deroin--Tholozan representations of punctured spheres. In particular, we prove that the action has no finite orbits if the underlying sphere has 7 punctures or more. When the sphere has six punctures, we show that there is a unique 1-parameter family of finite orbits. Our methods also recover Tykhyy's classification of finite orbits for 5-punctured spheres. The proof is inductive and uses Lisovyy--Tykhyy's classification of finite mapping class group orbits for 4-punctured spheres as the base case for the induction. Our results on Deroin--Tholozan representations cover the last missing cases to complete the proof of Tykhyy's Conjecture on finite mapping class group orbits for $\mathrm{SL}_2\mathbb{C}$ representations of punctured spheres, after the recent work by Lam--Landesman--Litt.

math.DS↗

arXiv2023

On Almost-Fuchsian submanifodls of Hadamard spaces and the asymptotic Plateau problem

We consider minimal submanifolds of negatively curved spaces with small curvature. We show that in a Hadamard space with negatively pinched curvature $-C\leq K\leq -1$, complete minimal submanifolds with second fundamental form less than $1$ everywhere bound a class of spheres at infinity for which the asymptotic Plateau problem is uniquely solvable.

math.DG↗

arXiv2023

On the Moser-Trudinger inequality for surfaces

This paper is devoted to the Moser-Trudinger inequality on smooth riemanniansurfaces. We establish that the constants involved can be chosen to depend on only 3parameters, which are the systole, isoperimetric constant and curvature of the surface. Wehave two analogous statements, considering respectively infinite-volume surfaces and closedsurfaces. As an application, we show that there are sequences of coverings of a hyperbolicclosed surface which admit a uniform Moser-Trudinger inequality.

math.DG↗

arXiv2023

Almost-fuchsian structures on disk bundles over a surface

Considering an integer $d>0$, we show the existence of convex-cocompactrepresentations of surface groups into SO(4,1) admitting an embedded minimal map withcurvatures in $(-1,1)$ and whose associated hyperbolic 4-manifolds are disk bundles of degreed over the surface, provided the genus $g$ of the surface is large enough. We also show that we can realize these representations as complex variation of Hodge structures. This gives examples of quasicircles in $\mathbb{S}^3$ bounding superminimal disks in $\mathbb{H}^4$ of arbitrarily small second fundamental form. Those are examples of generalized almost-Fuchsian representations which are not deformations of Fuchsian representations.

math.DG↗

arXiv2023

Maximal operators on hyperbolic triangles

We characterize the boundedness properties on the spaces $L^p(\mathbb{H}^2)$ of the maximal operator $M_\mathcal{B}$ where $\mathcal{B}$ is an arbitrary family of hyperbolic triangles stable by isometries.

math.CA↗

arXiv2023

On a convexity property of the space of almost fuchsian immersions

We study the space of Hopf differentials of almost fuchsian minimal immersions of compact Riemann surfaces. We show that the extrinsic curvature of the immersion at any given point is a concave function of the Hopf differential. As a consequence, we show that the set of all such Hopf differentials is a convex subset of the space of holomorphic quadratic differentials of the surface. In addition, we address the non-equivariant case, and obtain lower and upper bounds for the size of this set.

math.DG↗

arXiv2022

Bayesian inference in Epidemics: linear noise analysis

This paper offers a qualitative insight into the convergence of Bayesian parameter inference in a setup which mimics the modeling of the spread of a disease with associated disease measurements. Specifically, we are interested in the Bayesian model's convergence with increasing amounts of data under measurement limitations. Depending on how weakly informative the disease measurements are, we offer a kind of `best case' as well as a `worst case' analysis where, in the former case, we assume that the prevalence is directly accessible, while in the latter that only a binary signal corresponding to a prevalence detection threshold is available. Both cases are studied under an assumed so-called linear noise approximation as to the true dynamics. Numerical experiments test the sharpness of our results when confronted with more realistic situations for which analytical results are unavailable.

math.ST↗