arXiv research

Sharp heat kernel and Green's function estimates on Euclidean volume growth manifolds.

Sharp volume growth ratio for 3D manifolds with positive scalar curvature.

Sharp time analyticity proved for heat equation on Ricci solitons.

Sharp growth tightness proven for group quotients.

New hyperbolic manifolds show exponential homology torsion growth.

The study provides volume growth estimates for specific types of manifolds.

Investment strategy using fractional Kelly portfolios for better growth expectations.

Study on polynomial growth functions and forms on gradient Ricci solitons.

Study Liouville theorems for harmonic maps along ancient super Ricci flows.

Sharp Liouville theorem for minimal graphs on manifolds with nonnegative Ricci curvature.

Sharp bounds found for minimal surface solutions.

Ancient solutions to heat equations on graphs are shown to be analytic in time.

We prove sharp bounds for the growth rate of eigenfunctions of the Ornstein-Uhlenbeck operator and its natural generalizations. The bounds are sharp even up to lower order terms and have important applications to geometric flows.

For any manifold with polynomial volume growth, we show: The dimension of the space of ancient caloric functions with polynomial growth is bounded by the degree of growth times the dimension of harmonic functions with the same growth. As a consequence, we get a sharp bound for the dimension of ancient caloric functions…

Sharp estimate for nodal domains intersecting a ball on a Riemannian manifold.

Study polynomial growth harmonic functions on infinite penny graphs.

We obtain area growth estimates for constant mean curvature graphs in $\mathbb{E}(κ,τ)$-spaces with $κ\leq 0$, by finding sharp upper bounds for the volume of geodesic balls in $\mathbb{E}(κ,τ)$. We focus on complete graphs and graphs with zero boundary values. For instance, we prove that entire graphs in $\mathbb{E}(κ…

The classical Hadamard three circle theorem is generalized to complete Kähler manifolds. More precisely, we show that the nonnegativity of the holomorphic sectional curvature is a necessary and sufficient condition for the three circle theorem. As corollaries, two sharp monotonicity formulae for holomorphic functions a…

By applying an average method in PDE, we obtain a dichotomy between "constancy" and "infinity" of the warping functions on complete noncompact Riemannian manifolds for an appropriate isometric immersion of a multiply warped product manifold $N_1\times_{f_2} N_2 \times \cdots \times _{f_k} N_k\,$ into a Riemannian mani…

The paper proves conditions for isoperimetric regions in curved spaces.

Sharp Sobolev inequalities proved on manifolds with non-negative Ricci curvature.

Sharp isoperimetric inequality for Finsler manifolds with non-negative Ricci curvature.

The study examines polynomial growth functions on gradient shrinking Ricci solitons.

Sharp heat equation gradient estimates on compact manifolds.

Study growth rates of harmonic functions on curved surfaces.

Sharp inequality for submanifolds in manifolds with non-negative Ricci curvature.

We show that the martingale component in the long-term factorization of the stochastic discount factor due to Alvarez and Jermann (2005) and Hansen and Scheinkman (2009) is highly volatile, produces a downward-sloping term structure of bond Sharpe ratios, and implies that the long bond is far from growth optimality. In…

Let $M^n$ be a complete noncompact K$\ddot{a}$hler manifold of complex dimension $n$ with nonnegative holomorphic bisectional curvature. Denote by $\mathcal{O}$_d(M^n)$the space of holomorphic functions of polynomial growth of degree at most$d$on$M^n$. In this paper we prove that$dim_{\mathbb{C}}{\mathcal{O}}_d(…

In this paper, we discuss the self-shrinking systems in higher codimensional spaces. We mainly obtain several Bernstein type results and a sharp growth estimate.

The study examines complete Kähler manifolds with nonnegative Ricci curvature and discovers rigidity properties.

Framework generates realistic crop images for growth modeling.

We study minimal graphic functions on complete Riemannian manifolds $\Si$ with non-negative Ricci curvature, Euclidean volume growth and quadratic curvature decay. We derive global bounds for the gradients for minimal graphic functions of linear growth only on one side. Then we can obtain a Liouville type theorem with …

Anosov subgroups' deformations affect limit cones and growth indicators continuously.

We observe that a sharp result on the exponential growth rate of the number of primitive elements exists for the free group on two generators.

Ancient caloric functions on manifolds with polynomial growth are studied under volume doubling barrier.

We study solvency of insurers in a comprehensive model where various economic factors affect the capital developments of the companies. The main interest is in the impact of real growth to ruin probabilities. The volume of the business is allowed to increase or decrease. In the latter case, the study is focused on run-…

The paper examines eigenvalues and inequalities on Riemannian manifolds.

Establishes refined singularity estimate for nonnegative n-superharmonic functions in locally conformally flat manifolds.

This note addresses some questions that arise in the series of works by Kyoji Saito on the growth functions of graphs. We study "hyperbolike" graphs, which include Cayley graphs of hyperbolic groups. We generalize some well-known results on hyperbolic groups to the hyperbolike setting, including rationality of generati…

Uniqueness found for elliptic equations with drift on manifolds.

In this paper, we prove sharp gradient estimates for a positive solution to the heat equation $u_t=Δu+au\log u$ in complete noncompact Riemannian manifolds. As its application, we show that if $u$ is a positive solution of the equation $u_t=Δu$ and $\log u$ is of sublinear growth in both spatial and time directions the…

Paper proposes new strategies for better portfolio estimation in long-term investments with unknown distributions.

We show that gradient shrinking, expanding or steady Ricci solitons have potentials leading to suitable reference probability measures on the manifold. For shrinking solitons, as well as expanding soltions with nonnegative Ricci curvature, these reference measures satisfy sharp logarithmic Sobolev inequalities with low…

We prove the Turaev-Viro invariants volume conjecture for a "universal" class of cusped hyperbolic 3-manifolds that produces all 3-manifolds with empty or toroidal boundary by Dehn filling. This leads to two-sided bounds on the volume of any hyperbolic 3-manifold with empty or toroidal boundary in terms of the growth r…

Optimal estimates for spectral projection norms on compact manifolds.

Study sharp convergence rates of empirical UOT for spatio-temporal point processes.

We investigate fourth order Paneitz equations of critical growth in the case of $n$-dimensional closed conformally flat manifolds, $n \ge 5$. Such equations arise from conformal geometry and are modelized on the Einstein case of the geometric equation describing the effects of conformal changes of metrics on the $Q$-cu…

In this paper, we derive a new monotonicity formula for the plurisuhbarmonic functions on complete Kähler manifolds with nonnegative bisectional curvature. As applications we derive the sharp estimates for the dimension of the spaces of holomorphic functions (sections) with polynomial growth, which in particular, parti…