arXiv research

Study strict stability of cones with isolated singularities.

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.

Stability inequalities for specific solutions in high dimensions.

Local minimality proven for stable free-boundary minimal hypersurfaces.

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

We show that a strict, nearly Kähler $6$-manifold with either second or third Betti number nonzero is linearly unstable with respect to the $ν$-entropy of Perelman and hence is dynamically unstable for the Ricci flow.

The paper studies K-stability of spherical varieties and their degenerations.

Study shows how close functions are to optimal in Riemannian manifolds.

We investigate stability and local minimizing properties of the Riemannian functional defined by the L^p norm of the curvature tensor on the space of Riemannian metrics on a closed manifold. Riemannian metrics with constant curvature and products of such metrics are critical points of this functional. We prove that the…

The study proves uniqueness of large isoperimetric sets in specific noncompact manifolds.

New LP method recovers MAP solution from noisy stable instances.

The paper computes torsion invariants for groups acting on complexes.

The paper proves geometric inequalities and their stabilities for curves in hyperbolic space.

Study rigidity of minimal disks in specific 3-manifolds.

We show that the standard picture regarding the notion of stability of constant scalar curvature metrics in Kähler geometry described by S.K. Donaldson, which involves the geometry of infinite-dimensional groups and spaces, can be applied to the constant scalar curvature metrics in Sasaki geometry with only few modific…

The paper establishes conditions for strict power concavity in convolutions.

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

Study stability of selective SSMs with discontinuous gating.

LLMs fail to match statistical ground truth despite stable run-to-run performance.

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.

Sharp constants in curl-Sobolev inequalities on spheres determined.

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

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

Paper proves stability of solutions for specific hyperbolic systems.

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…

3D space stability confirmed for mass theorem.

Extends results on marginally outer trapped surfaces to general null expansion.

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…

We investigate rigidity and stability properties of critical points of quadratic curvature functionals on the space of Riemannian metrics. We show it is possible to "gauge" the Euler-Lagrange equations, in a self-adjoint fashion, to become elliptic. Fredholm theory may then be used to describe local properties of the m…

Study complex hyperbolic lattices and their relation to strict hyperbolization.

We prove extension theorems for several geometric properties such as asymptotic property C (APC), finite decomposition complexity (FDC), strict finite decomposition complexity (sFDC) which are weakenings of Gromov's finite asymptotic dimension (FAD). The context of all theorems is a finitely generated group $G$ with a …

In deterministic optimization, line searches are a standard tool ensuring stability and efficiency. Where only stochastic gradients are available, no direct equivalent has so far been formulated, because uncertain gradients do not allow for a strict sequence of decisions collapsing the search space. We construct a prob…

In deterministic optimization, line searches are a standard tool ensuring stability and efficiency. Where only stochastic gradients are available, no direct equivalent has so far been formulated, because uncertain gradients do not allow for a strict sequence of decisions collapsing the search space. We construct a prob…

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…

We introduce a geometrically transparent strict saddle property for nonsmooth functions. This property guarantees that simple proximal algorithms on weakly convex problems converge only to local minimizers, when randomly initialized. We argue that the strict saddle property may be a realistic assumption in applications…

SnareNet adds repair layers to neural networks to ensure outputs meet physical constraints.

Unified treatment of RC in stochastic and deterministic settings.

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…

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…

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

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…