arXiv research

Proves local maximizers for higher Ekeland-Hofer capacities in 4D star-shaped domains.

Local equivalence found between maximally symmetric rolling and flat Cartan distributions.

Study bifurcations and local rigidity on flag manifolds for Yamabe solutions.

Local equivalence shown between specific distributions and flat Cartan distribution.

New maximal surfaces solve Bernstein problems.

We show that, on a complete and possibly non-compact Riemannian manifold of dimension at least 2 without close conjugate points at infinity, the existence of a closed geodesic with local homology in maximal degree and maximal index growth under iteration forces the existence of infinitely many closed geodesics. For clo…

The function on the Teichmueller space of complete, orientable, finite-area hyperbolic surfaces of a fixed topological type that assigns to a hyperbolic surface its maximal injectivity radius has no local maxima that are not global maxima.

Locally maximizing orbits studied in twist maps and billiards.

Minimal energy local systems on curves are compact components of character varieties.

The paper proves finite topological type theorems for open manifolds with non-negative Ricci curvature and almost maximal local rewinding volume.

Study on geodesics in spacetime, proving properties of multiple maximizing paths.

New method tackles nonconvex-nonconcave problems with local KL condition.

The paper studies billiards in symmetric tables and finds a measure bound for maximizing orbits.

New method solves complex constrained optimization problems.

We introduce in this paper the concept of tropical mirror hypersurfaces and we prove a complex tropical localization Theorem which is a version of Kapranov's Theorem \cite{K-00} in tropical geometry. We give a geometric and a topological equivalence between coamoebas of complex algebraic hypersurfaces defined by a maxi…

Localized curvature bounds ensure harmonic maps are constant.

Directly estimates Fisher score for likelihood maximization.

We prove that every non-positively curved locally symmetric manifold M of finite volume contains a compact set K such that no periodic maximal flat can be homotoped out of K.

StoSOO optimistically maximizes noisy, locally smooth functions.

In this paper we introduce a local approach for the study of maximal surfaces immersed into a Lorentzian product space of the form $M^2\times R_1$, where $M^2$ is a connected Riemannian surface and $M^2\times R_1$ is endowed with the product Lorentzian metric. Specifically, we establish a local integral inequality for …

Graph products inherit Morse local-to-global property from their components.

We consider an online influence maximization problem in which a decision maker selects a node among a large number of possibilities and places a piece of information at the node. The node transmits the information to some others that are in the same connected component in a random graph. The goal of the decision maker …

The notion of maximal extension of a globally hyperbolic space-time arises from the notion of maximal solutions of the Cauchy problem associated to the Einstein's equations of general relativity. In 1969 Choquet-Bruhat and Geroch proved that if the Cauchy problem has a local solution, this solution has a unique maximal…

The Laplace spectrum uniquely identifies five out of eight metrically maximal three-dimensional geometries.

We classify (up to local isometry) the maximally supersymmetric solutions of the eleven- and ten-dimensional supergravity theories. We find that the AdS solutions, the Hpp-waves and the flat space solutions exhaust them.

Improves EM algorithm for better local optima in mixture models.

Classifies homogeneous CR hypersurfaces in low dimensions with maximal symmetry.

The paper proves the existence of boundary minimal hypersurfaces in compact manifolds with boundary.

For suitable metrics on the locally symmetric space associated to a maximal representation, we prove inequalities between the length of the boundary and the lengths of orthogeodesics that generalize the classical Basmajian's identity from Teichmueller theory. Any equality characterizes diagonal embeddings.

Study robust utility maximization with uncertain continuous semimartingales.

We prove that any minimal (maximal) strongly regular surface in the three-dimensional Minkowski space locally admits canonical principal parameters. Using this result, we find a canonical representation of minimal strongly regular time-like surfaces, which makes more precise the Weierstrass representation and shows mor…

Ricci flow shows PIC1 manifolds with maximal volume growth are like Euclidean space.

New method improves weakly-supervised action localization.

Study of area preserving Willmore flow on Schwarzschild-like manifolds.

We use maximal periodic flats to show that on a finite volume irreducible locally symmetric manifold of dimension $\geq 3$, no metric $g$ has more symmetry than the locally symmetric metric. We also show that if $g$ is a finite volume metric that is not locally symmetric, then its lift to the universal cover has discre…

New research proves uniqueness of maximal spacetime boundaries under certain conditions.

Over-parameterization helps EM avoid local optima in Gaussian mixture models.

New method for probabilistic clustering using matrix norm couplings.

Maximizes eigenvalue of Jacobi operator on spheres.

Geodesic flows on compact manifolds without conjugate points are shown to have a unique measure of maximal entropy.

New model shows VIX futures are more expensive than local volatility model suggests.

Extremal length systole is maximized at the Bolza surface.

Optimal algorithm for submodular maximization in distributed networked scenarios.

We construct canonical frames and find all maximally symmetric models for a natural generic class of corank 2 distributions on manifolds of odd dimension greater or equal to 7. This class of distributions is characterized by the following two conditions: the pencil of 2-forms associated with the corresponding Pfaffian …

Harmonic functions on Calabi-Yau manifolds with maximal volume growth are studied.

We prove that the next possible dimension after the maximal $n^2+2n$ for the Lie algebra of local projective symmetries of a metric on a manifold of dimension $n>1$ is $n^2-3n+5$ if the signature is Riemannian or $n=2$, $n^2-3n+6$ if the signature is Lorentzian and $n>2$, and $n^2-3n+8$ elsewise. We also prove that the…

We study 3-dimensional non-Riemannian Lorentz geometries, i.e. compact locally homogeneous Lorentz 3-manifolds with non-compact (local) isotropy group. One result is that, up to a finite cover, all such manifolds admit Lorentz metrics of (non-positive) constant sectionnal curvature. If the geometry is maximal, then the…

This paper is concerned with properties of maximal solutions of the Ricci and cross curvature flows on locally homogeneous three-manifolds of type SL(2,R). We prove that, generically, a maximal solution originates at a sub-Riemannian geometry of Heisenberg type. This solves a problem left open in earlier work by two of…