arXiv research

This paper proves properties of convex integrands and their duals.

Stable convex integrands are open and dense in smooth convex integrands.

The paper examines smoothness and stability of convex integrands and their duals.

In this paper, it is shown that a Wulff shape is strictly convex if and only if its convex integrand is of class $C^1$. Moreover, applications of this result are given.

Simplifies Wulff theorem for crystalline shapes using Minkowski Theory.

New geometric interpretations reveal structure of AC integrands.

Study on Gauss map of anisotropic minimal surfaces with Morse index estimates.

Chiral string integrands simplify to ambitwistor string integrands in the tensionless limit.

Kernel quadratures can be consistent even when the integrand is less smooth than assumed.

Quantum speedup for Monte Carlo integration reduces integrand calls.

Proves partial regularity and stratifies singular points for convex functionals.

Ambitwistor string matches superstring chiral integrands at zero tension.

In anomaly-free quantum field theories the integrand in the bosonic functional integral--the exponential of the effective action after integrating out fermions--is often defined only up to a phase without an additional choice. We term this choice ``setting the quantum integrand''. In the low-energy approximation to M-t…

Bayesian optimization for expensive integrands achieves optimal performance.

Extends Euler calculus to continuous integrands using curvature.

We study the pointwise supremum of convex integral functionals $\mathcal{I}_{f,γ}(ξ)= \sup_{Q} \left( \int_Ωf(ω,ξ(ω))Q(dω)-γ(Q)\right)$ on $L^\infty(Ω,\mathcal{F},\mathbb{P})$ where $f:Ω\times\mathbb{R}\rightarrow\overline{\mathbb{R}}$ is a proper normal convex integrand, $γ$ is a proper convex function on the set of p…

Novel approach for estimating conditional expectations using Bayesian quadrature.

In this paper we consider the evolution of a graph-like hypersurface by anisotropic mean curvature flow, under some restrictions on the anisotropic area integrand. We find interior estimates (in both time and space) on the gradient of such hypersurfaces, depending only on the height of the graph and the anisotropic are…

The goal of the present paper is to investigate the algebraic structure of global conformal invariants of submanifolds. These are defined to be conformally invariant integrals of geometric scalars of the tangent and normal bundle. A famous example of a global conformal invariant is the Willmore energy of a surface. In …

Counterexample shows Ito integrand needn't be locally square integrable.

Geometric proof shows regularity of anisotropic minimal surfaces in 2D.

Michael-Simon inequality proven for anisotropic energies close to area.

This paper forms part of a larger work where we prove a conjecture of Deser and Schwimmer regarding the algebraic structure of "global conformal invariants"; these are defined to be conformally invariant integrals of geometric scalars. The conjecture asserts that the integrand of any such integral can be expressed as a…

This work improves Fourier pricing for multi-asset options using RQMC with domain transformation.

Study proves uniform regularity for surface energies, critical and subcritical.

This is the second in a series of papers where we prove a conjecture of Deser and Schwimmer regarding the algebraic structure of ``global conformal invariants''; these are defined to be conformally invariant integrals of geometric scalars. The conjecture asserts that the integrand of any such integral can be expressed …

In this paper we study asymptotically hyperbolic manifolds given as graphs of asymptotically constant functions over hyperbolic space $\bH^n$. The graphs are considered as subsets of $\bH^{n+1}$ and carry the induced metric. For such manifolds the scalar curvature appears in the divergence of a 1-form involving the int…

Smooths basket option pricing for faster computation.

On a compact Kahler manifold, one can define global invariants by integrating local invariants of the metric. Assume that a global invariant thus obtained depends only on the Kahler class. Then we show that the integrand can be decomposed into a Chern polynomial (the integrand of a Chern number) and divergences of one …

This is the fifth in a series of papers where we prove a conjecture of Deser and Schwimmer regarding the algebraic structure of ``global conformal invariants''; these are defined to be conformally invariant integrals of geometric scalars. The conjecture asserts that the integrand of any such integral can be expressed a…

The study proves that certain minimal surfaces are flat under specific conditions.

Proves energy expression on Poincaré-Einstein spaces.

Positive weights improve kernel quadrature's accuracy.

Constructs polyhedral chains with prescribed tangent plane distributions.

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

In 1963, K.P.Grotemeyer proved an interesting variant of the Gauss-Bonnet Theorem. Let M be an oriented closed surface in the Euclidean space R^3 with Euler characteristic χ(M), Gauss curvature G and unit normal vector field n. Grotemeyer's identity replaces the Gauss-Bonnet integrand G by the normal moment <a,n>^2G, w…

We develop two types of integral formulas for the perimeter of a convex body K in planar geometries. We derive Cauchy-type formulas for perimeter in planar Hilbert geometries. Specializing to H^2 we get a formula that appears to be new. We show that it implies the standard Cauchy-Santalo formula involving a central ang…

Paper defines a pathwise Ito integral without probabilistic assumptions.

This is the first in a series of papers where we prove a conjecture of Deser and Schwimmer regarding the algebraic structure of ``global confor- mal invariants"; these are defined to be conformally invariant integrals of geometric scalars. The conjecture asserts that the integrand of any such integral can be expressed …

This is the fourth in a series of papers where we prove a conjecture of Deser and Schwimmer regarding the algebraic structure of ``global conformal invariants''; these are defined to be conformally invariant integrals of geometric scalars. The conjecture asserts that the integrand of any such integral can be expressed …

This is the last in a series of papers where we prove a conjecture of Deser and Schwimmer regarding the algebraic structure of ``global conformal invariants''; these are defined to be conformally invariant integrals of geometric scalars. The conjecture asserts that the integrand of any such integral can be expressed as…

The Gauss-Bonnet curvature of order $2k$ is a generalization to higher dimensions of the Gauss-Bonnet integrand in dimension $2k$, as the usual scalar curvature generalizes the two dimensional Gauss-Bonnet integrand. In this paper, we evaluate the first variation of the integrals of these curvatures seen as functionals…

NCV uses neural networks to improve Monte Carlo integration.

Study on error rates for approximating rough volatility models.

The paper analyzes kernel-based quadrature in misspecified settings, providing convergence rates and robustness conditions.

Local index theorem for chiral geometric operators proved using heat kernel.

Bayesian Quadrature speeds up integration by selecting batches of points instead of single points.

Extends stability approach to BSDEs with jumps, providing criteria for existence and uniqueness.