arXiv research

We propose a new notion called \emph{infinity-harmonic maps}between Riemannain manifolds. These are natural generalizations of the well known notion of infinity harmonic functions and are also the limiting case of $p$% -harmonic maps as $p\to \infty$. Infinity harmoncity appears in many familiar contexts. For example,…

Generalizes L-infinity spaces to sheaves over nilpotent dg manifolds.

A new definition of umbilic points at infinity for polynomial surfaces.

Paper uses Carleman estimates to study harmonic functions on surfaces at infinity.

The paper proves mapping class groups of closed surfaces are simply connected at infinity.

In this paper we mainly pay attention to the complex hyperbolic triangle groups of type (m, n, infinity) and discuss the discreteness. From the results more explicit conclusions about the triangle groups of type (n, infinity, infinity) will also be given.

This is a survey of the author's paper arXiv:1001.0023 on "Algebraic Geometry over C-infinity rings". If X is a smooth manifold then the R-algebra C^\infty(X) of smooth functions c : X --> R is a "C-infinity ring". That is, for each smooth function f : R^n --> R there is an n-fold operation Φ_f : C^\infty(X)^n --> C^\i…

We study connected sum at infinity on smooth, open manifolds. This operation requires a choice of proper ray in each manifold summand. In favorable circumstances, the connected sum at infinity operation is independent of ray choices. For each m at least 3, we construct an infinite family of pairs of m-manifolds on whic…

The paper examines mass aspects at future null infinity and limits of quasilocal mass.

The paper splits manifolds using infinity harmonic functions with linear growth.

We prove a version of the countable union theorem for asymptotic dimension and we apply it to groups acting on asymptotically finite dimensional metric spaces. As a consequence we obtain the following finite dimensionality theorems. A) An amalgamated product of asymptotically finite dimensional groups has finite asympt…

The paper defines curvature at infinity for flat manifolds.

Novel approach to wave equations near null infinity in flat spacetimes.

This paper explores A-infinity structures in contact categories and strand algebras.

Computes quasi-local mass at null infinity using Bondi-Sachs coordinates.

A Lie-infinity morphism relates derived Leibniz algebras from Maurer-Cartan elements.

The paper studies the structure at infinity of shrinking Ricci solitons with bounded curvature.

Nijenhuis forms help understand deformations of Lie algebroids and Poisson structures.

The paper analyzes null infinity's geometry without restrictions.

Paper constructs characteristic classes using C-infinity algebras.

We study the geometry at infinity of expanding gradient Ricci solitons of dimension greater than two with finite asymptotic curvature ratio without curvature sign assumptions. We mainly prove that they have a cone structure at infinity.

Researchers define and evaluate quasi-local mass near axially symmetric null infinity.

Let F be R or C, d the dimension of F over R. Denote by P(F) either the affine plane A(F) or the hyperbolic plane H(F) over F. An arrangement L of k lines in P(F) (pairwise non-parallel in the hyperbolic case) has a link at infinity K(L) comprising k unknotted (d-1)-spheres in the (2d-1)-sphere, whose topology reflects…

Local mass at null infinity confirmed for Vaidya spacetime.

Define mass invariant for asymptotically hyperbolic 3-manifolds with toroidal infinity.

Study asymptotic behavior of Weingarten surfaces at infinity.

Identifies scales in Ricci-flat manifolds at infinity.

The study proves rigidity for Poincaré-Einstein manifolds with flat Euclidean conformal infinity.

Positive injectivity radius for manifolds with Lie structure at infinity.

A C-infinity ring is a set equipped with n-ary operations corresponding to smooth n-ary functions on the real line (satisfying natural axioms). We prove that the cosimplicial abelian group associated to the de Rham complex of Euclidean space has the structure of a cosimplicial C-infinity ring. We also analyse the notio…

Defines tensor products for A-infinity structures using diagonals.

Minimal hypersurfaces scarring along a fixed one in certain manifolds.

What are called secondary characteristic classes in Chern-Weil theory are a refinement of ordinary characteristic classes of principal bundles from cohomology to differential cohomology. We consider the problem of refining the construction of secondary characteristic classes from cohomology sets to cocycle spaces; and …

We investigate existence and uniqueness of bounded solutions of parabolic equations with unbounded coefficients in $M\times \mathbb R_+$, where $M$ is a complete noncompact Riemannian manifold. Under specific assumptions, we establish existence of solutions satisfying prescribed conditions at infinity, depending on the…

For a polynomial $f$ in two complex variables, we prove that the multi-link at infinity of the 0-fiber $f^{-1}(0)$ is a fibred multi-link if and only if all the values different from 0 are regular at infinity.

Analytic sets with unique infinite tangent cone are algebraic.

The procedure "Lie group --> Lie algebra" has a generalization "simplicial manifold --> L_infinity algebra", or yet better, "presheaf on the category of surjective submersions --> L_infinity algebra". We describe this generalization, together with its higher-order extensions.

In the Cauchy problem for asymptotically flat vacuum data the solution-jets along the cylinder at space-like infinity develop in general logarithmic singularities at the critical sets at which the cylinder touches future/past null infinity. The tendency of these singularities to spread along the null generators of null…

Researchers calculate limits of angular momentum and center-of-mass at null infinity.

Ecker's and Huisken's quantities agree for ancient mean curvature flows.

We define the notion of action of an L-infinity algebra $g$ on a graded manifold $M$, and show that such an action corresponds to a homological vector field on $g[1] \times M$ of a specific form. This generalizes the correspondence between Lie algebra actions on manifolds and transformation Lie algebroids. In particula…

The study examines entropy and pressure at infinity in negatively curved manifolds, linking them to strong positive recurrence.

Study of tangent cones at infinity for algebraic sets.

Study steady gradient Ricci solitons with cylindrical tangent flows at infinity.

Unique global solutions found for specific initial data.

New Einstein metrics created by modifying hyperbolic infinity.

Riemannian manifolds can be sphere at infinity of certain solitons.

Unique solutions found for wave-like decaying null infinity equations.