arXiv research

Constructs entropy-minimizing pseudo-Anosov diffeomorphisms on K3 surfaces.

Study Liouville action for harmonic maps between Riemann surfaces.

Complex surfaces show non-simply connected diffeomorphism groups with non-homotopic loops.

For a non-orientable closed surface standardly embedded in the 4-sphere, a diffeomorphism over this surface is extendable if and only if this diffeomorphism preserves the Guillou-Marin quadratic form of this embedded surface.

An orientation preserving diffeomorphism over a surface embedded in a 4-manifold is called extendable, if this diffeomorphism is a restriction of an orientation preserving diffeomorphism on this 4-manifold. In this paper, we investigate conditions for extendability of diffeomorphisms over surfaces in the complex projec…

Exotic diffeomorphisms found on complex surfaces and 4-manifolds.

Classifies periodic diffeomorphisms and hyperelliptic involutions on surfaces.

Minimal Lagrangian diffeomorphisms between spherical surfaces are rigid.

The volume conjecture is extended for surface diffeomorphisms with quantum invariants.

We answer affirmatively a question posed by Morita on homological stability of surface diffeomorphisms made discrete. In particular, we prove that $C^{\infty}$-diffeomorphisms and volume preserving diffeomorphisms of surfaces as family of discrete groups exhibit homological stability. We show that the stable homology o…

This paper extends quasimorphism results to nonorientable surfaces.

We prove a number of results on the interrelation between the $L^p$-metric on the group of Hamiltonian diffeomorphisms of surfaces and the subset of all autonomous Hamiltonian diffeomorphisms. More precisely, we show that there are Hamiltonian diffeomorphisms of all surfaces of genus $g\neq 1$ lying arbitrarily $L^p$-f…

The study explores how surface diffeomorphisms of knots relate to their topological properties.

Short proof shows infinite diameter for surface diffeomorphisms.

Study curvatures of diffeomorphisms on non-orientable surfaces.

Elliptic surfaces have unique Lefschetz pencils and Calabi-Yau diffeomorphisms.

In this paper we prove that no complex surface of general type is diffeomorphic to a rational surface, thereby completing the smooth classification of rational surfaces and the proof of the Van de Ven conjecture on the smooth invariance of Kodaira dimension.

The volume conjecture for surface diffeomorphisms connects volumes to polynomial evaluations.

Triangulates surfaces with bounded energy using diffeomorphisms.

New counterexample shows curved surfaces can deform geodesics without diffeomorphism.

Study shows Hamiltonian diffeomorphisms form a connected component in $C^0$-topology for most symplectic rational surfaces.

Surface corks modify 4-manifold structures without changing their homeomorphism type.

Authors prove existence of exotic surfaces and invariants not detecting self-diffeomorphisms.

Classifies periodic diffeomorphisms on surfaces commuting with specific involutions.

We present a new method to compare the shapes of genus-zero surfaces. We introduce a measure of mutual stretching, the symmetric distortion energy, and establish the existence of a conformal diffeomorphism between any two genus-zero surfaces that minimizes this energy. We then prove that the energies of the minimizing …

The aim of this paper is to show the rigidity of homologically trivial actions of prime order on K3 surfaces. To be precise, we show that homotopy K3 surfaces do not admit a periodic diffeomorphism of odd prime order 3 acting trivially on cohomology. Moreover, we give an obstruction in terms of the rationality and sign…

Affine diffeomorphisms are undistorted in half-translation surfaces.

We prove that the entropy norm on the group of diffeomorphisms of a closed orientable surface of positive genus is unbounded.

A surface in the 4-sphere is trivially embedded, if it bounds a 3-dimensional handle body in the 4-sphere. For a surface trivially embedded in the 4-sphere, a diffeomorphism over this surface is extensible if and only if this preserves the Rokhlin quadratic form of this embedded surface.

The paper shows how Hamiltonian diffeomorphisms and homeomorphisms can be broken down into smaller, manageable pieces.

Paper proves every stable 4-sphere has a unique diffeomorphism class.

Embedding calculus proves convergence for surfaces.

The paper proposes a deep learning approach to efficiently approximate diffeomorphisms for shape alignment.

Study on mapping classes of real rational surface automorphisms, focusing on reducible maps and pseudo-Anosov maps.

The paper constructs diffeomorphisms on a $G_2$-manifold achieving entropy bounds.

We show that the action of Cremona transformations on the real points of quadrics exhibits the full complexity of the diffeomorphisms of the sphere, the torus, and of all non-orientable surfaces. The main result says that if X is rational, then Aut(X), the group of algebraic automorphisms, is dense in Diff(X), the grou…

Study decomposes geometric surfaces, finding special curves.

We answer a question posed by Morita concerning the non-triviality of certain secondary characteristic classes for surface bundles. In doing so we are naturally led to show that a form of Harer stability holds for surface diffeomorphism groups in homology of small degree.

We prove the existence of a minimal diffeomorphism isotopic to the identity between two hyperbolic cone surfaces $(Σ,g_1)$ and $(Σ,g_2)$ when the cone angles of $g_1$ and $g_2$ are different and smaller than $π$. When the cone angles of $g_1$ are strictly smaller than the ones of $g_2$, this minimal diffeomorphism is u…

The study finds points on surfaces where a tensor is conformal to a metric.

Let f:Σ_1 --> Σ_2 be an area preserving diffeomorphism between compact Riemann surfaces of constant curvature. The graph of f can be viewed as a Lagrangian submanifold in Σ_1\times Σ_2. This article discusses a canonical way to deform f along area preserving diffeomorphisms. This deformation process is realized through…

Maximal dilatation found on nonorientable surfaces.

The paper proves a factorization theorem for harmonic maps between Riemann surfaces and manifolds.

Given a simply-connected closed 4-manifold $X$ and a smoothly embedded oriented surface $Σ$, various constructions based on Fintushel-Stern knot surgery have produced new surfaces in $X$ that are pairwise homeomorphic to $Σ$, but not diffeomorphic. We prove that for all known examples of surface knots constructed from …

Study shows complex K3 surfaces have infinite free abelian subgroup in their diffeomorphism group.

Authors prove quantum invariant conjecture for figure-eight knot complement.

We introduce a new invariant, the real (logarithmic)-Kodaira dimension, that allows to distinguish smooth real algebraic surfaces up to birational diffeomorphism. As an application, we construct infinite families of smooth rational real algebraic surfaces with trivial homology groups, whose real loci are diffeomorphic …

A homeomorphism of a compact metric space is {\em tight} provided every non-degenerate compact connected (not necessarily invariant) subset carries positive entropy. It is shown that every $C^{1+α}$ diffeomorphism of a closed surface factors to a tight homeomorphism of a generalized cactoid (roughly, a surface with nod…