arXiv research

New geometric interpretations reveal structure of AC integrands.

Constructs polyhedral chains with prescribed tangent plane distributions.

Study proves uniform ellipticity implies uniform polyconvexity for anisotropic energy functionals.

Polyconvex energies with conformal invariance have smooth stationary points outside a discrete set.

We study integrals of the form $\int_Ωf\left( dω\right)$, where $1\leq k\leq n$, $f:Λ^{k}\rightarrow\mathbb{R}$ is continuous and $ω$ is a $\left(k-1\right)$-form. We introduce the appropriate notions of convexity, namely ext. one convexity, ext. quasiconvexity and ext. polyconvexity. We study their relations, give sev…

The paper establishes conditions for strict power concavity in convolutions.

The paper studies strict equivalence in multi-virtual linkoids with new invariants.

Study strict stability of cones with isolated singularities.

We introduce a more restrictive version of the strict $CD(K,\infty)$ -condition, the so-called very strict $CD(K,\infty)$ -condition, and show the existence of optimal maps in very strict $CD(K,\infty)$ -spaces despite the possible lack of uniqueness of optimal plans.

Maps Lie 2-groups to Weil algebras, showing cohomology isomorphisms.

Proves integrability of strict Lie 2-algebras using cohomological methods.

We study strict local martingales via h-transforms, a method which first appeared in Delbaen-Schachermayer. We show that strict local martingales arise whenever there is a consistent family of change of measures where the two measures are not equivalent to one another. Several old and new strict local martingales are i…

In an earlier work, we constructed the almost strict Morse $n$-category $\mathcal X$ which extends Cohen $\&$ Jones $\&$ Segal's flow category. In this article, we define two other almost strict $n$-categories $\mathcal V$ and $\mathcal W$ where $\mathcal V$ is based on homomorphisms between real vector spaces and $\ma…

Proximal methods avoid local minima in weakly convex problems.

Study complex hyperbolic lattices and their relation to strict hyperbolization.

In this paper, we initiate the study of a parametrised version of Rieffel's strict deformation quantization. We apply it to give a classification of noncommutative principal torus bundles, in terms of parametrised strict deformation quantization of ordinary principal torus bundles. The paper also contains a putative de…

There are two major streams of literature on the modeling of financial bubbles: the strict local martingale framework and the Johansen-Ledoit-Sornette (JLS) financial bubble model. Based on a class of models that embeds the JLS model and can exhibit strict local martingale behavior, we clarify the connection between th…

New insights into matrix factorization show strict saddles have bounded eigenvalues.

In this paper, we use the parametrised strict deformation quantization of C*-bundles obtained in a previous paper, and give more examples and applications of this theory. In particular, it is used here to classify H_3-twisted noncommutative torus bundles over a locally compact space. This is extended to the case of gen…

Proves strict inequality for minimizers of Willmore energy under isoperimetric constraints.

Study on Kähler manifolds sharing submanifolds, proving projective implies relative.

We present simple new examples of pure-jump strict local martingales. The examples are constructed as exponentials of self-exciting affine Markov processes. We characterize the strict local martingale property of these processes by an integral criterion and by non-uniqueness of an associated ordinary differential equat…

Strict type-II blowup in harmonic map flow is proven to have Hölder continuous body map.

New methods help escape strict saddle points in nonsmooth optimization.

Let X be a norm curve in the SL(2,C)-character variety of a knot exterior M. Let t = || b || / || a || be the ratio of the Culler-Shalen norms of two distinct non-zero classes a, b in H_1(\partial M, Z). We demonstrate that either X has exactly two associated strict boundary slopes \pm t, or else there are strict bound…

We present explicit universal strict deformation quantization formulae for actions of Iwasawa subgroups AN of SU(1,n). This answers a question raised by Rieffel.

We show the equivalence of the definitions of very strict $CD(K,N)$ -condition defined, on one hand, using (only) the entropy functionals, and on the other, the full displacement convexity class $\mathcal{DC}_N$. In particular, we show that assuming the convexity inequalities for the critical exponent implies it for al…

In discrete time markets with proportional transaction costs, Schachermayer (2004) shows that robust no-arbitrage is equivalent to the existence of a strictly consistent price system. In this paper, we introduce the concept of prospective strict no-arbitrage that is a variant of the strict no-arbitrage property from Ka…

We consider implied volatilities in asset pricing models, where the discounted underlying is a strict local martingale under the pricing measure. Our main result gives an asymptotic expansion of the right wing of the implied volatility smile and shows that the strict local martingale property can be determined from thi…

There are two parts of this paper. First, we discovered an explicit formula for the complex Hessian of the weighted log-Bergman kernel on a parallelogram domain, and utilised this formula to give a new proof about the strict convexity of the Mabuchi functional along a smooth geodesic. Second, when a C^{1,1}-geodesic co…

A strict local martingale is a local martingale which is not a martingale. There are few explicit examples of "naturally occurring" strict local martingales with jumps available in the literature. The purpose of this paper is to provide such examples, and to illustrate how they might arise via filtration shrinkage, a p…

We prove that two links related by a surgery along a connected, strict graph clasper of degree n are C_n-equivalent, i.e, related by a sequence of surgeries along strict tree claspers of degree n.

We consider a simple instance of action up to homotopy. More precisely, we consider strict actions of DGLAs in degrees -1 and 0 on degree 1 NQ-manifolds. In a more conventional language this means: strict actions of Lie algebra crossed modules on Lie algebroids. When the action is strict, we show that it integrates to …

For d < 5, we describe an elementary construction of nonzero degree, strict contractions between closed, oriented hyperbolic d-oribifolds. Appealing to work of Gueritaud-Kassel and Tholozan, these examples determine exotic quotients of SO_0(d,1).

Paper introduces Atiyah sequence for Lie groupoids and studies gauge transformations.

This work is a contribution to the area of Strict Quantization (in the sense of Rieffel) in the presence of curvature and non-Abelian group actions. More precisely, we use geometry to obtain explicit oscillatory integral formulae for strongly invariant strict deformation quantizations of a class of solvable symplectic …

Gradient descent can use larger step sizes to avoid strict saddle points.

We build a concrete and natural model for the strict 2-category of orbifolds. In particular we prove that if one localizes the 2-category of proper etale Lie groupoids at a class of 1-arrows that we call "covers", then the strict 2-category structure drops down to the localization. In our construction the spaces of 1- …

Strict convexity of graphs with constant mean curvature is proven under certain conditions.

We study the stability of non compact steady and expanding gradient Ricci solitons. We first show that strict linear stability implies dynamical stability. Then we give various sufficient geometric conditions ensuring the strict linear stability of such gradient Ricci solitons.

New boundary condition for Black-Scholes equations in strict local martingale models.

Proves hyperbolized groups are virtually compact special and linear.

Contact group retracts to unitary subgroup.

We exhibit sufficient conditions such that components of a multidimensional SDE giving rise to a local martingale $M$ are strict local martingales or martingales. We assume that the equations have diffusion coefficients of the form $σ(M_t,v_t),$ with $v_t$ being a stochastic volatility term.

Study of gauge theory and parallel transport in Lie 2-group bundles over Lie groupoids.

It is conjectured that every cusped hyperbolic 3-manifold has a decomposition into positive volume ideal hyperbolic tetrahedra (a "geometric" triangulation of the manifold). Under a mild homology assumption on the manifold we construct topological ideal triangulations which admit a strict angle structure, which is a ne…

Lagrangian submanifolds in strict nearly Kähler 6-manifolds are related to special Lagrangian submanifolds in Calabi-Yau 6-manifolds and coassociative cones in $G_2$-manifolds. We prove that the mean curvature of a Lagrangian submanifold $L$ in a nearly Kähler manifold $(M^{2n}, J, g)$ is symplectically dual to the Mas…

Strict partial order is a mathematical structure commonly seen in relational data. One obstacle to extracting such type of relations at scale is the lack of large-scale labels for building effective data-driven solutions. We develop an active learning framework for mining such relations subject to a strict order. Our a…