A singularity theorem based on asymptotic volume growth
problem Proving singularity theorems
method Introducing asymptotic volume-expansion invariants
result Proving an explicit upper bound on the time-separation from a hypersurface to its chronological past
Investigates quadratic-exponential growth BSDEs with jumps and proves existence and differentiability.
problem Existence and differentiability of solutions to quadratic-exponential growth BSDEs with jumps.
method Proves existence and differentiability of solutions under general quadratic-exponential structure using local Lipschitz continuity and A_gamma-condition.
result Proves existence and differentiability of solutions under general quadratic-exponential structure.
Bubbles are essential in certain economic models with high growth and low interest rates.
problem Asset price bubbles exceeding fundamental values.
method Developed the Bubble Necessity Theorem in economic models with specific growth and interest rate conditions.
result Bubbles are inevitable in certain economic scenarios with high growth and low interest rates.
SGD converges fast for over-parameterized models.
problem Training highly expressive models that fit data perfectly.
method Constant step-size SGD with Nesterov acceleration.
result Matches deterministic accelerated method's convergence rate.
The paper is concerned with the problem of existence of solutions for the Heath-Jarrow-Morton equation with linear volatility. Necessary conditions and sufficient conditions for the existence of weak solutions and strong solutions are provided. It is shown that the key role is played by the logarithmic growth condition…
The US GDP per capita growth alternates between high and low rates, with an average growth rate of 1.6% since 1800.
problem Understanding the fluctuations and stability of US GDP growth rates over time.
method Wavelet transform analysis of US GDP per capita data from 1800 to 2010.
result The growth rate of US GDP per capita is bimodal, alternating between high and low rates with an average of 1.6% since 1800.
Groups with hyperbolic properties don't have strong Property (T).
problem Proving groups with hyperbolic properties don't have strong Property (T).
method Constructing an unbounded affine representation with polynomial growth.
result Groups with hyperbolic properties do not have strong Property (T).
Study strong max principle for vector maps on curved spaces.
problem Characterize vector valued harmonic maps with linear growth.
method Apply strong max principle to maps on manifolds with non-negative Ricci curvature.
result Equalities among supremum, asymptotic average, and heat evolution of map norms.
Proves Zimmer's conjecture for certain lattice actions on low-dimensional manifolds.
problem Zimmer's conjecture for higher-rank lattices on low-dimensional manifolds.
method Uniform subexponential growth of derivatives, strong property (T), and homogeneous dynamics.
result Finite image of homomorphisms for certain actions.
P.W. Anderson proposed the concept of complexity in order to describe the emergence and growth of macroscopic collective patterns out of the simple interactions of many microscopic agents. In the physical sciences this paradigm was implemented systematically and confirmed repeatedly by successful confrontation with rea…
The aim of this paper is to state and prove polynomial analogues of the classical Manning inequality relating the topological entropy of a geodesic flow with the growth rate of the volume of balls in the universal covering. To this aim we use two numerical conjugacy invariants, the {\em strong polynomial entropy $h_{po…
Study growth rates of harmonic functions on curved surfaces.
problem Understanding the growth rates of harmonic functions on curved surfaces.
method Gradient estimate and frequency analysis on complete surfaces and manifolds with non-negative curvature.
result Existence and properties of nonconstant polynomial growth harmonic functions on manifolds with maximal volume growth.
New minimal surfaces grow area very quickly.
problem Understanding minimal surfaces with rapid area growth.
method Examples of minimal immersions in Euclidean space.
result Proper minimal surfaces with rapid area growth found.
New results on homology torsion growth for various groups.
problem Understanding the growth of higher torsion homologies for arithmetic lattices and other groups.
method Quantitative homotopical method called effective rebuilding, constructing small classifying spaces of finite index subgroups.
result Strong asymptotic bounds for the torsion growth in principal congruence subgroups.
Given for instance a finite volume negatively curved Riemannian manifold M, we give a precise relation between the logarithmic growth rates of the excursions into cusps neighborhoods of the strong unstable leaves of negatively recurrent unit vectors of M and their linear divergence rates under the geodesic flow. As…
We investigate the relation between economic growth and equality in a modified version of the agent-based asset exchange model (AEM). The modified model is a driven system that for a range of parameter space is effectively ergodic in the limit of an infinite system. We find that the belief that "a rising tide lifts all…
We propose a novel approach and an empirical procedure to test direct contagion of growth rate in a trade credit network of firms. Our hypotheses are that the use of trade credit contributes to contagion (from many customers to a single supplier - "many to one" contagion) and amplification (through their interaction wi…
Using the classical approach we show the existence of disc type solutions to the asymptotic Plateau problem in certain Hadamard manifolds which may have arbitrarily strong curvature and volume growth.
Study finds minimal hypersurfaces grow linearly in index, contrary to 3D.
problem Understanding index growth of minimal hypersurfaces.
method Partitioning methods for compact Lie groups, applied to hypersurfaces.
result Linear index growth for hypersurfaces of fixed topological type.
Study maximum likelihood estimator for growth rate of jump-type CIR process.
problem Estimating growth rate of jump-type CIR process from continuous observations.
method Maximum likelihood approach, distinguishing subcritical, critical, and supercritical cases.
result Asymptotic properties including consistency and normality for different cases.
The goal of this paper is to prove a result conjectured in Föllmer and Schachermayer [FS07], even in slightly more general form. Suppose that S is a continuous semimartingale and satisfies a large deviations estimate; this is a particular growth condition on the mean-variance tradeoff process of S. We show that S then …
Polynomial growth bounds for eigenfunctions on non-compact spaces.
problem Growth of eigenfunctions on non-compact spaces with Gaussian weight.
method Analyzing non-compact manifolds with Gaussian weight and drift Laplacian.
result Showed same polynomial growth bounds as Euclidean space for general tensors.
We establish new strong lower bounds on the (subnormal) subgroup growth of a large class of groups. This includes the fundamental groups of all finite-volume hyperbolic 3-manifolds and all (free non-abelian)-by-cyclic groups. The lower bound is nearly exponential, which should be compared with the fastest possible subg…
Framework generates realistic crop images for growth modeling.
problem Modeling crop growth over time with precision and detail.
method Two-stage framework: image prediction and growth estimation models.
result Framework accurately predicts crop images with varying conditions.
New method approximates quadratic-growth BSDEs with short-term expansions.
problem Approximating solutions to quadratic-growth Backward Stochastic Differential Equations (BSDEs).
method Connecting semi-analytic asymptotic expansions over short-time intervals.
result Avoids Monte Carlo simulation and numerical integrations for estimating conditional expectations.
Improved SGD methods converge faster for nonconvex optimization.
problem Nonconvex optimization challenges in machine learning.
method Adaptive SGD with line-search and Polyak stepsizes.
result Unified convergence rates for various nonconvex functions.
Minimal volume entropy vanishes or is positive under certain fiber growth conditions.
problem Conditions for minimal volume entropy to be zero or positive.
method Analyzes topological conditions related to fiber growth of maps.
result Examples of finite simplicial complexes with zero simplicial volume and large minimal volume entropy.
Paper improves Stein property for certain Kahler manifolds.
problem Complete open Kahler manifolds with positive bisectional curvature being Stein.
method Restricts volume growth condition to a weaker one.
result Improves previous observation on Stein property.
We investigate the hierarchical structures of countries based on electricity consumption and economic growth by using the real amounts of their consumption over a certain time period. We use of electricity consumption data to detect the topological properties of 60 countries from 1971 to 2008. These countries are divid…
Sharp time analyticity proved for heat equation on Ricci solitons.
problem Analyticity of heat equation solutions on gradient shrinking Ricci solitons.
method Proved analyticity for solutions with quadratic exponential growth.
result Sharp growth condition for analyticity is established.
This paper proposes a continuous timing strategy for growth vs. defensive style allocation.
problem Dynamic allocation of growth and defensive ETF baskets using macro-market timing signals.
method Continuous smooth score combining multiple factors, mapped to G/D weights, smoothed with EWMA.
result Continuous style timing strategy outperforms static benchmarks in risk-adjusted returns.
We consider a general class of diffusion-based models and show that, even in the absence of an Equivalent Local Martingale Measure, the financial market may still be viable, in the sense that strong forms of arbitrage are excluded and portfolio optimisation problems can be meaningfully solved. Relying partly on the rec…
In this paper we study volume growth of gradient steady Ricci solitons. We show that if the potential function satisfies a uniform condition, then the soliton has at most Euclidean volume growth.
Climate volatility reduces economic growth, especially in poorer countries.
problem Impact of climate volatility on economic growth.
method Exploiting data on 133 countries over 59 years, controlling for temperature changes.
result A 1 degree C increase in temperature volatility leads to a 0.3% decline in GDP growth.
We prove that any gradient shrinking Ricci soliton has at most Euclidean volume growth. This improves a recent result of H.-D. Cao and D. Zhou by removing a condition on the growth of scalar curvature.
Study explores Liouville's theorem and SLP for harmonic functions on cones and surfaces.
problem Investigating Liouville's theorem and SLP for harmonic functions on Riemannian cones and surfaces.
method Reinterprets classical Liouville property in terms of radial eigenfunctions, providing explicit estimates and constructing examples.
result Explicit estimates for slowest-growing nonconstant harmonic functions and a unified geometric perspective on Liouville phenomena.
Study on MLE growth rate for stable CIR process, proving consistency and normality.
problem Estimating the growth rate of a stable CIR process from continuous observations.
method Maximum likelihood estimation for a specific type of process.
result Strong consistency and asymptotic normality in subcritical and supercritical cases, asymptotic mixed normality in supercritical, open in critical case.
Study volume growth and asymptotic cones of nonnegative Ricci curvature manifolds.
problem Whether the volume growth order of manifolds is greater than or equal to the dimension of their asymptotic cones.
method Analyzing asymptotic cones and volume growth conditions, extending Sormani's results.
result Existence of asymptotic cones with upper box dimension at most equal to the volume growth order.
Harmonic functions on compact symmetric spaces exhibit strong convexity properties.
problem Understanding the convexity of harmonic functions on compact symmetric spaces.
method Analyzing the nonnegativity of the Laplacian powers of harmonic functions.
result Harmonic functions on compact symmetric spaces have nonnegative Laplacian powers, demonstrating strong convexity.
The study analyzes firm/city growth models leading to Zipf distributions.
problem Analyzing firm/city growth patterns and their distribution.
method Analytical model based on multi-item criterion for entity selection.
result Stationary size distribution is generically a Zipf-law under certain conditions.
Study Liouville theorems for harmonic maps along ancient super Ricci flows.
problem Proving Liouville theorems for harmonic maps under specific geometric conditions.
method Using Perelman's reduced geometric viewpoint, derive Liouville theorems with controlled growth.
result Sharp growth conditions and new Liouville theorems for both non-positively and positively curved target spaces.
The paper explores geometric influences on PDE solutions on manifolds.
problem Qualitative behavior of solutions to quasilinear PDEs on Riemannian manifolds.
method Investigates strong and weak maximum principles, compact support principles, and Liouville theorems.
result Identifies thresholds involving curvatures or volume growth to guarantee properties under Keller-Osserman conditions.
Study of stochastic differential equations on non-compact manifolds, solving open problem on strong completeness.
problem Open problem on strong completeness of SDEs on non-compact spaces.
method Systematic study of stochastic differential equations, solving open problem on strong completeness.
result Existence of global smooth solution flow of SDEs on R^n, including substantial growth of coefficients.
We prove flatness of complete Riemannian planes and cylinders without conjugate points under optimal conditions on the area growth.
The study examines entropy and pressure at infinity in negatively curved manifolds, linking them to strong positive recurrence.
problem Investigating strong positive recurrence in negatively curved manifolds.
method Defining and comparing entropy and pressure at infinity through different measures.
result Strong positive recurrence potentials admit finite Gibbs measures.
We prove weak and strong maximum principles, including a Hopf lemma, for smooth subsolutions to equations defined by linear, second-order, partial differential operators whose principal symbols vanish along a portion of the domain boundary. The boundary regularity property of the smooth subsolutions along this boundary…
In this article, we solve the strong openness conjecture on the multiplier ideal sheaves for the plurisubharmonic functions posed by Demailly. We prove two conjectures about the growth of the volumes of the sublevel sets of plurisubharmonic functions related to the complex singularity exponents and quasi-plurisubharmon…
We investigate the optimal strategy over a finite time horizon for a portfolio of stock and bond and a derivative in an multiplicative Markovian market model with transaction costs (friction). The optimization problem is solved by a Hamilton-Bellman-Jacobi equation, which by the verification theorem has well-behaved so…