Study fiber-preserving, orientation-reversing involutions on Seifert fibered 3-manifolds.
problem Characterize fiber-preserving, orientation-reversing involutions on Seifert fibered 3-manifolds.
method Construct a class of involutions, extend product involutions, and use double covering.
result Any fiber-preserving, orientation-reversing involution factors as a product of an orientation-preserving and a specific class of involutions.
Maps between certain Lipschitz manifolds are isometries if they preserve volume.
problem Volume preservation and isometry conditions for Lipschitz manifolds.
method Volume-preserving 1-Lipschitz maps from integral currents onto infinitesimally Euclidean Lipschitz manifolds.
result Volume-preserving maps are isometries under given conditions.
DMT enhances deep neural networks to better preserve data structures.
problem Preserving geometric, topological, and distributional structures of data in NLDR.
method Deep manifold transformation (DMT) using cross-layer LGP constraints.
result DMT networks outperform existing NLDR methods in preserving data structures.
Classifies geodesic-preserving bijections in Thurston geometries.
problem Identifying bijections that preserve geodesics in different geometries.
method Comprehensive classification and proof for various geometries.
result Complete classification of geodesic-preserving bijections in Thurston geometries.
The paper studies quasimorphisms on density-preserving diffeomorphisms of the Möbius band.
problem Exploring quasimorphisms on groups of diffeomorphisms of non-orientable manifolds.
method Investigates the group of density-preserving diffeomorphisms on the Möbius band and shows the existence of unbounded quasimorphisms.
result The group of density-preserving diffeomorphisms on the Möbius band admits countably many unbounded quasimorphisms.
Heat flow fails to preserve concavity in curved spaces.
problem Non-preservation of concavity properties in curved spaces.
method Analysis of Dirichlet heat flow on Riemannian manifolds.
result No concavity properties are preserved unless curvature is zero.
Proves rigidity of certain transformations on specific geometric manifolds.
problem Rigidity of conformal circle-preserving transformations on Berwaldian manifolds.
method Analyzes properties of Berwaldian manifolds and flag curvatures.
result Rigidity condition for nontrivial conformal circle-preserving transformations.
Paper shows L∞-positivity and stochastic completeness are equivalent.
problem Analyzing L∞-positivity preserving property and stochastic completeness. method Using monotone approximation results for distributional solutions of −Δ+1≥0. result The L∞-positivity preserving property is equivalent to stochastic completeness. Paper proposes a new method for supervised manifold learning using random forest proximities.
problem Existing supervised manifold learning methods fail to uncover meaningful embeddings due to using class-conditional distances.
method Proposes a data-geometry-preserving variant of random forest proximities as an initialization for manifold learning methods.
result Local and global structure preservation is near universal across manifold learning approaches using diffusion-based algorithms.
Study generalizes map properties between Hermitian manifolds preserving specific forms.
problem Understanding maps between Hermitian manifolds that preserve certain forms.
method Generalizing results from Chan-Yuan [2025] to new maps.
result Obtained further rigidity and non-existence theorems.
The theory of product preserving functors and Weil functors is partly extended to infinite dimensional manifolds, using the theory of C∞-algebras.
New invariants defined for volume-preserving flows on 3-manifolds.
problem Defining invariants for volume-preserving flows.
method Extending wrapping number and trunk to define invariants of links and flows.
result Wrappingness and trunkenness are not functions of helicity.
The paper proves positivity preservation and self-adjointness for Schrödinger operators on incomplete Riemannian manifolds.
problem Positivity preservation and self-adjointness for Schrödinger-type operators on incomplete Riemannian manifolds.
method Control of potential behavior near the Cauchy boundary, essential self-adjointness proof, core of smooth compactly supported functions.
result Positivity preservation and essential self-adjointness of Schrödinger operators on Lp functions on incomplete Riemannian manifolds. Preserves hyperbolicity in link complements with two moves.
problem Maintaining hyperbolicity in link complements.
method Chain move and switch move to preserve hyperbolicity.
result Preserves hyperbolicity in a substantial number of links.
GCML preserves geometric structure in manifold clustering for diverse data types.
problem Loss functions in manifold clustering can corrupt latent space structure.
method GCML framework with isometric and ranking losses for geometric structure preservation.
result GCML outperforms other methods in latent space structure preservation and performance metrics.
Curvature regularization prevents distortion in graph embeddings.
problem Graph topology patterns distort in Euclidean space, making detection difficult.
method Proposes curvature regularization to enforce flatness in embedding manifolds.
result Significant improvements in five embedding methods on open graph datasets.
Mutation is an operation on 3-manifolds containing an embedded surface of genus 2. It is defined by cutting along the surface and regluing using the `hyperelliptic' involution, and is known to preserve many 3-manifold invariants. I show that mutation of a homology 3-sphere preserves its (instanton) Floer homology, and …
Constructs deformations of Vaisman manifolds preserving foliations.
problem Deforming Vaisman manifolds while maintaining their canonical foliations.
method Uses a basic 1-form with specific properties to construct transverse deformations.
result Basic 1-forms exist in abundance for constructing deformations.
Local holomorphic maps preserving (p,p) forms are shown to be isometries.
problem Preserving (p,p) forms under holomorphic maps between Kähler manifolds.
method Analyzing local holomorphic maps between Kähler manifolds, proving isometries up to scalars.
result Holomorphic maps preserving (p,p) forms are isometries under certain conditions.
We study the area preserving Willmore flow in an asymptotic region of an asymptotically flat manifold which is C3−close to Schwarzschild. It was shown by Lamm, Metzger and Schulze that such an end is foliated by spheres of Willmore type. In this paper, we prove that the leaves of this foliation are stable under sm…
We consider some natural infinitesimal Einstein deformations on Sasakian and 3-Sasakian manifolds. Some of these are infinitesimal deformations of Killing spinors and further some integrate to actual Killing spinor deformations. In particular, on 3-Sasakian 7 manifolds these yield infinitesimal Einstein deformations pr…
In this paper we introduce a general notion of weak extension property for embeddings induced by a group actions. As an example, for the group H(M, m) of measure-preserving homeomorphisms of a noncompact manifold M, we deduce weak type extension theorems, and as an application we exhibit the local contractibility of th…
New method learns identity-preserving transformations on data manifolds without labels.
problem Learning identity-preserving transformations on natural variations without supervision.
method Introduces a learning strategy that does not require transformation labels and learns local regions for operators.
result Trains on MNIST and Fashion MNIST, and CelebA, learning transformations without labels.
Isometries of metric spaces (X,d) preserve all level sets of d. We formulate and prove cases of a conjecture asserting if X is a complete Riemannian manifold, then a function f:X→X preserving at least one level set d−1(r), with r>0 small enough, is an isometry.
In a paper published in 2002, the author gave a criterion to determine whether there is a fiber-preserving branched covering between two given orientable Seifert manifolds with orientable bases. Here we supply some details of the proof of two claims in that paper. We give an explicit construction of fiber-preserving br…
This paper describes a characterization of tightness of closed contact 3-manifolds in terms of supporting open book decompositions. The main result is that tightness of a closed contact 3-manifold is preserved under Legendrian surgery.
The study preserves lower bounds of total scalar curvature under specific metric convergence.
problem Preserving lower bounds of total scalar curvature on smooth manifolds.
method Used stability of Ricci flow and heat flow with Ricci flow background.
result Lower bound of weighted total scalar curvature is preserved under specified convergence conditions.
In two previous papers the author presented a general construction of finite, fiber- and orientation-preserving group actions on orientable Seifert manifolds. In this paper we restrict our attention to elliptic 3-manifolds. A proof is given that orientation-reversing and fiber-preserving diffeomorphisms of Seifert mani…
Knots in 3-manifolds are equivalent if isotopic, except in special cases.
problem Understanding when knots in 3-manifolds are equivalent and isotopic.
method Analyzing prime, closed, oriented 3-manifolds and irreducible manifolds, and considering orientation-preserving mapping class groups and homeomorphisms.
result Knots in prime, closed, oriented 3-manifolds are isotopic if and only if the orientation preserving mapping class group is trivial.
The paper studies Ricci flow on manifolds with boundary, proving existence, uniqueness, and boundary conditions preservation.
problem Ricci flow on manifolds with boundary.
method Proving short-time existence and uniqueness of the solution, and showing boundary conditions preservation.
result The flow preserves natural boundary conditions under certain curvature conditions.
The study shows finite measure-preserving isometry groups for certain metric measure spaces.
problem Understanding the structure of isometry groups in metric measure spaces.
method Analyzing synthetic negative Ricci curvature and Bakry-Émery Ricci curvature.
result The measure-preserving isometry group is finite for compact metric measure spaces with specific curvature conditions.
We prove that any real-analytic, volume-preserving action of a lattice Γ in a simple Lie group with $\Qrank(Γ)\geq 7$ on a closed 4-manifold of nonzero Euler characteristic factors through a finite group action.
This paper extends the results from the author's previous paper to consider finite, fiber- and orientation- preserving group actions on closed, orientable Seifert manifolds M that fiber over a non-orientable base space. An orientable base space double cover M~ of M is constructed and then an isomorphism be…
Unified theory of measure-preserving diffusions on manifolds.
problem Deriving a complete recipe for measure-preserving diffusions on manifolds.
method Developed a geometric theory that unifies and generalizes previous constructions, relying on intrinsic geometry of the target measure.
result The completeness result is a direct consequence of manifold topology and target measure geometry.
R-circles in general three dimensional CR manifolds (of contact type) are the analogues to traces of Lagrangian totally geodesic planes on the sphere viewed as the boundary of two dimensional complex hyperbolic space. They form a family of certain legendrian curves on the manifold. We prove that a diffeomorphism betwee…
New method preserves topology in Hodge decomposition for scalar and vector fields.
problem Topology-preserving Hodge decomposition on manifolds with boundaries.
method Comprehensive 5-component decomposition in Eulerian representation.
result Effective numerical experiments validate the method's accuracy and orthogonality.
Develops integrators for Hamiltonian systems in Jacobi manifolds.
problem Modeling conservative systems with dissipative and thermodynamic phenomena.
method Constructs structure-preserving integrators for Hamiltonian systems in Jacobi manifolds.
result Proposes a numerical integration technique compatible with Jacobi dynamics.
We provide a variational description of any Liouville (i.e. volume preserving) autonomous vector fields on a smooth manifold. This is obtained via a ``maximal degree'' variational principle; critical sections for this are integral manifolds for the Liouville vector field. We work in coordinates and provide explicit for…
Compact Finslerian manifolds don't admit non-trivial circle-preserving transformations.
problem Characterizing Finslerian manifolds without circle-preserving transformations.
method Analyzing critical points of conformal transformations to prove manifold rigidity.
result Compact Finslerian manifolds are Riemannian and conformally diffeomorphic to standard spheres, Euclidean spaces, or hyperbolic spaces.
The paper proves a conjecture about positivity preserving in Riemannian manifolds.
problem Proving positivity preserving for Lp functions on Riemannian manifolds. method New a-priori regularity result, Liouville type theorem, Brezis-Kato inequality.
result Proves a conjecture by M. Braverman, O. Milatovic, and M. Shubin (2002).
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…
In this paper, we establish the rigidity result for local holomorphic volume preserving maps from an irreducible Hermitian manifold of compact type into its Cartesian products.
Bi-Lipschitz Autoencoder ensures robust manifold preservation.
problem Non-injective autoencoders lead to poor convergence and distorted latent representations.
method Injective regularization and bi-Lipschitz relaxation.
result BLAE consistently outperforms existing methods in manifold preservation.
Study of parabolic-preserving deformations of hyperbolic lattices.
problem Preserving parabolic subgroups during lattice deformations.
method Analysis of deformations into SU(n,1) and SO(n+1,1).
result Existence of 1-parameter families of parabolic-preserving deformations.
Study shows decay of correlations on specific types of flows.
problem Analyzing decay of correlations in specific flow types.
method Asymptotic expansion of correlation function on Abelian covers.
result Established an expansion in inverse powers of time.
The following result is proved: Consider a 4-dimensional Kaehler manifold M with nonvanishing Bochner tensor B. Then any holomorphic transformation of M, which preserves B is a homothety.
We show that the set of the equivalence classes of multifoliate structures is in one-to-one correspondence with the set of equivalence classes of finite complete projective systems of vector space epimorphisms. After that we give the complete description of all product preserving bundle functors on the categories of mu…
We consider a connected smooth n-dimensional manifold M endowed with a volume form Ω, and we show that an open subset U of Rn of Lebesgue measure $\Vol (U)$ embeds into M by a smooth volume preserving embedding whenever the volume condition $\Vol (U) \le \Vol (M,Ω)$ is met.