arXiv research

In this paper, we study deformations of compact holomorphic Poisson submanifolds which extend Kodaira's series of papers on semi-regularity (deformations of compact complex submanifolds of codimension 1), deformations of compact complex submanifolds of arbitrary codimensions, and stability of compact complex submanifol…

In this article, we consider Cayley deformations of a compact complex surface in a Calabi--Yau four-fold. We will study complex deformations of compact complex submanifolds of Calabi--Yau manifolds with a view to explaining why complex and Cayley deformations of a compact complex surface are the same. We in fact prove …

Study deformations of compact Kähler hyperbolic manifolds.

In this thesis, we study deformations of compact holomorphic Poisson manifolds and algebraic Poisson schemes in the framework of Kodaira-Spencer's analytic deformation theory and Grothendieck's algebraic deformation theory.

Study deformations of compact Calabi-Yau conifolds with singularities.

The paper extends Witten's deformation to foliations and Morse functions.

The paper constructs metrics on compact manifolds using Aubin's deformations.

We combine classic stability results for foliations with recent results on deformations of Lie groupoids and Lie algebroids to provide a cohomological characterization for rigidity of compact foliations on compact manifolds.

Study on a deformed Hermitian-Yang-Mills equation on compact Kähler manifolds.

The paper studies deformations of cohesive modules on complex manifolds.

Develops a method to deform metrics on manifolds with non-compact boundaries.

Study on deforming calibrated submanifolds with boundary constraints.

Study on deformations of symmetric spaces using Jordan algebras.

Study resolves conjectures on hypercritical deformed Hermitian-Yang-Mills equation.

We introduce K-deformations of generalized complex structures on a compact Kahler manifold $M=(X, J)$ with an effective anti-canonical divisor and show that obstructions to K-deformations of generalized complex structures on $M$ always vanish. Applying the stability theorem of generalized Kahler structures, together wi…

In this paper, we prove several formulas related to Hodge theory, and using them to prove the deformations of a compact $H$-twisted generalized Calabi-Yau manifold are unobstructed and $L^2$ convergence in a neighborhood in another power series . And if we assume that the deformation is smooth in a fixed neighborhood, …

Researchers derived heat kernel expansions for non-compact spaces using Witten deformation.

Study of deformed Bott-Chern cohomology on complex manifolds.

The study explores deformations of discrete subgroups in non-compact homogeneous spaces.

Compact hyperbolic complex manifolds are rigid under deformation.

This paper shows similarities in deformation spaces of Kleinian groups and anti-holomorphic maps.

Compact metric f-K-contact manifolds constructed via specific transformations.

Study shows compact Sasakian manifolds are locally Heisenberg up to deformation.

In this note we prove that, under a weak condition, small deformations of a compact balanced manifold are also balanced. This condition is satisfied on the twistor space over a compact self-dual four manifold.

Solves supercritical dHYM on projective manifolds with specific conditions.

Obstructing deformations of vector forms on Kähler manifolds.

Localized deformation of scalar curvature and mean curvature on manifolds.

New method deforms function algebras on manifolds using spectral decomposition.

Study curvatures on compact pseudo-Hermitian manifolds using special methods.

The paper studies deformations of symplectic forms and Lagrangian submanifolds.

Let $G$ be a noncompact real algebraic group and $\G<G$ a lattice. One purpose of this paper is to show that there is an smooth, volume preserving, mixing action of $G$ or $\G$ on a compact manifold which admits a smooth deformation. We also describe some other, rather special, deformations when $G=SO(1,n)$ and provide…

The paper studies deformations of astheno-Kähler metrics on complex manifolds.

We study infinitesimal Einstein deformations on compact flat manifolds and on product manifolds. Moreover, we prove refinements of results by Koiso and Bourguignon which yield obstructions on the existence of infinitesimal Einstein deformations under certain curvature conditions.

Study deformed Hermitian-Yang-Mills equation on complex projective space blowup.

Let $X$ be a compact quotient of the product of the real Heisenberg group $H_{4m+1}$ of dimension $4m+1$ and the 3-dimensional real Euclidean space $\bR^3$. A left invariant hypercomplex structure on $H_{4m+1}\times \bR^3$ descends onto the compact quotient $X$. The space $X$ is a hyperholomorphic fibration of 4-tori o…

Deformations of compact Riemann surfaces are considered using a Čech cohomology sliding overlaps approach. Cocycles are calculated for conformal cutting and regluing deformations at zeros of Abelian differentials. A second order deformation expansion is presented for the Riemann period matrix. A complete deformation ex…

Deformations of singular Cayley submanifolds studied.

For arbitrary compact quantizable Kaehler manifolds it is shown how a natural formal deformation quantization (star product) can be obtained via Berezin-Toeplitz operators. Results on their semi-classical behaviour (their asymptotic expansion) due to Bordemann, Meinrenken and Schlichenmaier are used in an essential man…

The paper proves stability for contact groupoids and deformations.

Suppose that a compact quantum group Q acts faithfully and isomet- rically (in the sense of [10]) on a smooth compact, oriented, connected Riemannian manifold M . If the manifold is stably parallelizable then it is shown that the compact quantum group is necessarily commutative as a C \ast algebra i.e. Q = C(G) for som…

Study second-order obstruction to nearly $G_2$ structure deformations.

Study on symplectic structures and their deformations.

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

By using Klein's model for hyperbolic geometry, hyperbolic structures on orbifolds or manifolds provide examples of real projective structures. By Andreev's theorem, many 3-dimensional reflection orbifolds admit a finite volume hyperbolic structure, and such a hyperbolic structure is unique. However, the induced real p…

In this article, I prove the following statement: Every compact complex surface with even first Betti number is deformation equivalent to one which admits an extremal Kähler metric. In fact, this extremal Kähler metric can even be taken to have constant scalar curvature in all but two cases: the deformation equivalence…

The paper improves embedding results for $CR$ submanifolds, showing that compact deformations stay embeddable.

McLean studied the deformations of compact special Lagrangian submanifolds, showing in particular that they come in moduli spaces whose dimension depends only on the topology of the submanifold. In this article we study the analogous problem for non-compact, "asymptotically conical" SL submanifolds, with respect to var…

Study disproves conjecture about Hermitian-Yang-Mills solutions.