arXiv research

Sharp bounds found for energy in projective space mappings.

Hong Kong uses reference class forecasting to improve roadwork project cost and duration estimates.

In this paper we study the set of projective maps between compact proper convex real projective manifolds. We show that this set contains only finitely many distinct homotopy classes and each homotopy class has the structure of a real projective manifold. When the target manifold is strictly convex, our results imply t…

Holomorphic projective structures and bundles are studied on surfaces, revealing affine spaces of parameters.

Paper finds a divisibility property of first Pontrjagin classes for even-dimensional homotopy complex projective spaces.

Positive projectively flat metrics on Hopf manifolds are locally conformally flat-Kähler.

Optimizes energy of mappings from complex projective spaces.

Stability results for complex Monge-Ampère equations in various classes.

In this paper, we study a class of Finsler metrics composed by a Riemann metric $α=\sqrt{a_{ij}(x)y^i y^j}$ and a $1$-form $β=b_i(x)y^i$ called general ($α$, $β$)-metrics. We classify those projectively flat when $α$ is projectively flat. By solving the corresponding nonlinear PDEs, the metrics in this class are totall…

The paper defines a new equivalence relation for knot projections and finds an infinite number of distinct classes.

Study shows zero Pontrjagin classes for sprays.

The equation determining whether a projective structure admits a connection in its given projective class that has skew-symmetric Ricci tensor is an overdetermined system of semi-linear partial differential equations which we call the projective Einstein-Weyl (pEW) equation. In 2-dimensions, we give local obstructions …

The projective Finsler metrizability problem deals with the question whether a projective-equivalence class of sprays is the geodesic class of a (locally or globally defined) Finsler function. In this paper we use Hilbert-type forms to state a number of different ways of specifying necessary and sufficient conditions f…

A major source of risk in project management is inaccurate forecasts of project costs, demand, and other impacts. The paper presents a promising new approach to mitigating such risk, based on theories of decision making under uncertainty which won the 2002 Nobel prize in economics. First, the paper documents inaccuracy…

Paper introduces new Finsler metrics preserved under projective transformations.

PPF uses projections to improve classification accuracy.

FROCC uses random projections for fast one-class classification.

Study non-vanishing $\ell^2$-Betti numbers for specific groups.

The paper stratifies projective measured laminations and identifies a group of transformations.

A result about projections of Gibbs measures from a particular class arising in economic modeling is proved.

Extends K-stability theory to projective klt pairs with a big anticanonical class.

Study projective and almost conformally symplectic structures on manifolds.

New classes generalize Chern classes in supergeometry.

Paper tackles multi-label zero-shot learning, improving label embedding projection for unseen classes.

PCA outperforms random projections in retaining second order signals from latent groups.

Only products of projective lines have vanishing Futaki invariants for all Kähler classes.

Characterizes projective submanifolds in high dimensions.

Projective varieties remain stable under close polarizations, extending to Kähler cones.

Holonomy map is a local biholomorphism for parabolic projective structures on non-compact surfaces.

It is well known that pseudo-Riemannian metrics in the projective class of a given torsion free affine connection can be obtained from (and are equivalent to) the solutions of a certain overdetermined projectively invariant differential equation. This equation is a special case of a so-called first BGG equation. The ge…

A projection maps geodesic currents to Teichmüller space.

Unique maximal curve systems found for up to 5 punctures.

Enhances projection pursuit tree classifier with visual diagnostics for better multi-class classification.

Study on moduli spaces of branched projective structures on surfaces.

Sharp-SSL uses random projections to identify important variables for semi-supervised learning.

Sharp Lp affine isoperimetric inequalities are established for the entire class of Lp projection bodies and the entire class of Lp centroid bodies. These new inequalities strengthen the Lp Petty projection and the Lp Busemann--Petty centroid inequality.

Study estimates risks of nuclear waste storage projects.

The curve complex of a 3-holed projective plane is shown to be quasi-isometric to a tree and its automorphisms are isomorphic to the mapping class group.

Researchers calculate alpha invariant for certain complex projective spaces.

Singular Finsler metrics, such as Kropina metrics and $m$-Kropina metrics, have a lot of applications in the real world. In this paper, we study a class of singular Finsler metrics defined by a Riemann metric $α$ and 1-form $β$ and characterize those which are respectively Douglasian and locally projectively flat in di…

Exploits class similarity for better machine learning models with confidence labels and projective loss functions.

We prove Chern class equalities for abelian families with a holomorphic normal projective connection.

Researchers confirm a 15-vertex triangulation of the quaternionic projective plane is minimal.

Study projective KLT varieties with projectively flat cotangent sheaves.

Study on existence of weighted extremal Kähler metrics on projective bundles.

We extend the holomorphic analytic torsion classes of Bismut and Köhler to arbitrary projective morphisms between smooth algebraic complex varieties. To this end, we propose an axiomatic definition and give a classification of the theories of generalized holomorphic analytic torsion classes for arbitrary projective mor…

Exam project proof of Markov's Theorem.

The paper calculates the mapping class group of specific complex projective plane bundles.