arXiv research

New CR-structures lemma simplifies CR-manifold deformation proof.

Twilled L(ie-)R(inehart)-algebras generalize, in the Lie-Rinehart context, complex structures on smooth manifolds. An almost complex manifold determines an "almost twilled pre-LR algebra", which is a true twilled LR-algebra iff the almost complex structure is integrable. We characterize twilled LR structures in terms o…

Twilled L(ie)-R(inehart) algebas generalize, in the Lie-Rinehart context, complex structures on smooth manifolds. An almost complex manifold determines an almost twilled pre-LR algebra, which is a true twilled LR-algebra iff the almost complex structure is integrable. We characterize twilled LR-structures in terms of c…

We prove an analog of the Tian-Todorov theorem for twisted generalized Calabi-Yau manifolds; namely, we show that the moduli space of generalized complex structures on a compact twisted generalized Calabi-Yau manifold is unobstructed and smooth. We also construct the extended moduli space and study its Frobenius struct…

Researchers calculate exact moduli for type II flux backgrounds using spectral sequences.

In \cite{Goto}, Ryushi Goto has constructed the deformation space for a manifold equipped with a collection of closed differential forms and showed that in some important cases (Calabi-Yau, $G_2$- and $Spin(7)$-structures) this deformation space is smooth. This result unifies the classical Bogomolov-Tian-Todorov and Jo…

Introduces new holomorphic contact structures and proves unobstructedness theorems.

Explains the Schwarz lemma in lecture notes.

Author provides an alternate proof of the free ribbon lemma.

The paper extends Schwarz's lemma to RC-positivity and complex manifolds.

Survey on strong closing lemmas in Hamiltonian dynamics.

Study several weak forms of a lemma on compact complex manifolds.

Unified Schwarz lemma in Kähler and Hermitian geometry.

Paper generalizes Schwarz Lemma for VT harmonic maps with conditions.

Formulates Index III lemma and Rauch III theorem with applications.

New Schwarz Lemma for Bergman metrics in bounded domains.

Tucker and Ky Fan's lemma are combinatorial analogs of the Borsuk-Ulam theorem (BUT). In 1996, Yu. A. Shashkin proved a version of Fan's lemma, which is a combinatorial analog of the odd mapping theorem (OMT). We consider generalizations of these lemmas for BUT-manifolds, i.e. for manifolds that satisfy BUT. Proofs rel…

Paper proves a discrete Schwarz-Pick lemma for generalized circle packings.

The paper improves Zakalyukin's lemma for frontals and applies it to surface singularities.

Meridian lemma extended to fully alternating links in thickened surfaces.

Proves a quantitative closing lemma for negatively curved manifolds.

Paper generalizes Schwarz lemma for harmonic maps between Riemannian manifolds.

Extends Margulis Lemma to RCD(K,N) spaces.

The paper characterizes when the $\partial \overline{\partial}$-lemma holds for twistor spaces.

For a symplectic manifold $(M,ω)$, not necessarily hard Lefschetz, we prove a version of the Merkulov $dδ$--lemma. We also study the $dδ$--lemma and related cohomologies for compact symplectic solvmanifolds.

Positive representations on surfaces have positive cross-ratios and satisfy a collar lemma.

Proves a generalized Whitehead cut vertex lemma for tree groups.

Proves a general ∂∂̄-lemma and applies it to a Fujino conjecture.

Enhanced Schwarz lemma for Hermitian manifolds with new curvature constraints.

In this paper we will introduce a new notion of geometric structures defined by systems of closed differential forms in term of the Clifford algebra of the direct sum of the tangent bundle and the cotangent bundle on a manifold. We develop a unified approach of a deformation problem and establish a criterion of unobstr…

Schwarz lemma extended to equality cases and curvature on manifolds.

Generalized Stacey-Roberts lemma for Banach manifolds.

Thurston's jiggling lemma simplifies triangulations.

Extends Stein's lemma to exponential-family mixtures for gradient computation.

Abstract: Generalizes Milnor-Schwarz lemma to inverse monoids.

The paper extends the Discrete Schwarz-Pick Lemma to circle packings with obtuse intersections and disjoint packings.

For the convenience of readers of the article {\em No-arbitrage pricing under systemic risk: accounting for cross-ownership} (Fischer, 2012, arXiv:1005.0768), a full proof of Lemma A.5 and a shorter proof of Lemma A.6 of that paper are provided.

New proof and insights on Elliptical Potential Lemma for online learning.

We observe that Whitehead's lemma is an immediate consequence of Stallings folds.

The paper examines Kodaira dimensions of specific complex 4-manifolds with torsion first Chern class.

This paper proves an $C^{\infty}$ closing lemma for Hamiltonian flows on symplectic 4-manifolds.

Develops a generalized version of Chung's Lemma for stochastic optimization methods.

In this article, we prove an analog of the classical collar lemma in the setting of Hitchin representations.

The $L^2$-$\partial\overline\partial$-Lemma is extended to complete Kähler manifolds with a gap in the spectrum.

The famous Švarc-Milnor Lemma says that a group $G$ acting properly and cocompactly via isometries on a length space $X$ is finitely generated and induces a quasi-isometry equivalence $g\to g\cdot x_0$ for any $x_0\in X$. We redefine the concept of coarseness so that the proof of the Lemma is automatic.

New CR almost Schur Lemma estimates curvature on compact manifolds.

Simplified proof of Morrey's lemma for metric spaces.

Paper extends Weyl's lemma to RCD(K,N) spaces.