Study connects Chern class components to Kato surface germs.
problem Understanding intermediate Kato surfaces through Chern class components.
method Relates coefficients of Chern classes to birational germs.
result Established relations between Chern class components and Kato surface germs.
We give a homological construction of aperiodic tiles for certain open Riemannian surfaces admitting actions of Grigorchuk groups of intermediate growth.
Sparse curves on surfaces grow at a specific intermediate rate.
problem Understanding growth patterns of sparse curve systems on surfaces.
method Analyzing the intersection numbers and sizes of sparse curve systems.
result Sparse curve systems grow roughly like c g c^{\sqrt{g}} c g . Investigate pseudoconvexity of locally trivial holomorphic ball bundles over compact Riemann surfaces.
problem Pseudoconvexity of locally trivial holomorphic ball bundles over compact Riemann surfaces.
method Prove that any such bundle is 1-convex, while its complement is n-convex.
result Prove that any such bundle is 1-convex, while its complement is n-convex.
We investigate bi-Hermitian metrics on compact complex surfaces with odd first Betti number producing new examples with connected anti-canonical divisor using the general construction of \cite{abd15}. The result is a complete classification for all \it unbranched \rm Kato surfaces and a classification up to logarithmic…
The paper explores squircles and their 3D applications.
problem None explicitly stated; focuses on squircle equations and 3D surfaces.
method Examined and discussed squircle equations, then developed 3D surfaces based on these shapes.
result Developed 3D surfaces based on squircle equations.
New research shows all intermediate subgroups of braid groups are not bi-orderable.
problem Understanding bi-orderability of braid groups and their subgroups.
method Analyzing pure and full braid groups of various surfaces.
result Intermediate subgroups of braid groups are not bi-orderable.
Proves effective slope gaps for lattice surfaces.
problem Proving effective slope gaps for lattice surfaces.
method Proves effective slope gap distribution for square torus and general lattice surfaces.
result Effective slope gap distribution result for lattice surfaces.
Spaces of circle embeddings in curved surfaces indexed by trees.
problem Classifying spaces of braided automorphism groups of trees.
method Indexed connected components with finite rooted trees, constructed strong deformation retract.
result Connected components are classifying spaces of braided automorphism groups.
Paper investigates reflection principles for zero mean curvature surfaces in isotropic 3-space.
problem Investigating reflection principles for zero mean curvature surfaces in isotropic 3-space.
method Analyzes reflection principles for zero mean curvature surfaces in I 3 \mathbb{I}^3 I 3 . result Shows a reflection principle for isotropic line segments on zero mean curvature surfaces in I 3 \mathbb{I}^3 I 3 . The study finds a way to create minimal surfaces with specific shapes in 3-manifolds.
problem Creating minimal surfaces with prescribed genus in 3-manifolds with positive Ricci curvature.
method Develops a min-max theory and shows deformability of surfaces in a generic metric.
result Establishes a theorem for producing minimal surfaces with prescribed genus.
Defines kappa classes on KSBA spaces, generalizing classes on curves.
problem Generalizing Miller-Morita-Mumford classes to KSBA stable varieties and pairs.
method Defining kappa classes on KSBA moduli spaces and computing them in specific cases.
result Computed kappa classes on Campedelli surfaces, including finding the Chow ring of a specific GIT quotient.
We show that any grafting ray in Teichmüller space is (strongly) asymptotic to some Teichmüller geodesic ray. As an intermediate step we introduce surfaces that arise as limits of these degenerating Riemann surfaces. Given a grafting ray, the proof involves a Teichmüller ray with a conformally equivalent limit, and bui…
The compact curves of an intermediate Kato surface S S S form a basis of H 2 ( S , Q ) H^2(S,\mathbb Q) H 2 ( S , Q ) . We present a way to compute the associated rational coefficients of the first Chern class c 1 ( S ) c_1(S) c 1 ( S ) . We get in particular a simple geometric obstruction for c 1 ( S ) c_1(S) c 1 ( S ) to be an integral class, or equivalently index ( S ) = 1 (S)=1 ( S ) = 1 . We also f…
Study proves rigidity of minimal hypersurfaces in specific manifolds.
problem Proving rigidity of complete free boundary minimal hypersurfaces.
method Warped θ θ θ -bubble method, generalizing capillary surfaces. result No complete two-sided stable free boundary immersions in unit ball of R 4 \mathbb{R}^4 R 4 . This paper generalizes the envelope of mid-lines to intermediate lines for a plane curve.
problem Understanding the envelope of intermediate lines for a plane curve.
method Using singularity theory techniques to analyze the local behavior of the envelope of intermediate lines.
result The envelope of intermediate lines ( E I L EIL E I L ) is formed by three disconnected sets: AEIL, the curve itself, and IPTL. Study on rigidity with non-negative intermediate curvature on low-dimensional manifolds.
problem Extending non-existence theorem of positive scalar curvature to product manifolds.
method Introduced intermediate curvature and studied rigidity conditions.
result Rigidity when intermediate curvature is non-negative in low dimensions.
Preserves positive intermediate curvature on manifolds.
problem Obstructs positive intermediate curvature on partial tori.
method Shows smooth interpolation of metrics with positive intermediate curvature.
result Proves non-existence of certain manifolds with positive intermediate curvature.
Given a completely arbitrary surface, whether or not it has bounded curvature, or even whether or not it is complete, there exists an instantaneously complete Ricci flow evolution of that surface that exists for a specific amount of time [GT11]. In the case that the underlying Riemann surface supports a hyperbolic metr…
The study connects manifold topology to metrics with positive intermediate curvature.
problem Understanding the relationship between manifold topology and metrics with positive intermediate curvature.
method Formulated a conjecture and proved it for specific dimensions and conditions.
result Closed, aspherical 6-manifolds cannot admit metrics with positive 4-intermediate curvature.
Soft cells fill space without gaps, derived from minimal surfaces and deformed using edge bending.
problem Creating space-filling shapes without sharp corners.
method Edge bending algorithm to deform polyhedral tilings into soft tilings.
result Soft tilings derived from minimal surfaces can be continuously transformed into one another.
Develops a new non-abelian framework for Riemann surfaces and differential equations.
problem Analyzing second-order differential equations on Riemann surfaces.
method Gauge-theoretic framework and non-abelian approach.
result Extends Dedekind's Schwarzian approach to generic one-parameter families of curves of genus g.
New rigidity results for manifolds with maximal symmetry rank and positive intermediate Ricci curvature.
problem Understanding the structure of manifolds with maximal symmetry rank and positive intermediate Ricci curvature.
method Recovering stronger topological rigidity results using higher intermediate Ricci curvatures and nontrivial fundamental groups.
result Stronger topological rigidity results for manifolds with maximal symmetry rank and positive intermediate Ricci curvature.
Constructs correspondences on hyperelliptic surfaces combining orbifold groups and Blaschke products.
problem Combining geometric and dynamical properties on hyperelliptic surfaces.
method Analytic combinations on Riemann sphere, algebraic characterization, and Teichmüller spaces.
result Explicit description of correspondences and injection into Hurwitz spaces.
Study on spaces of metrics with intermediate curvature bounds.
problem Understanding spaces of metrics with lower bounds on intermediate curvatures.
method Analyzing spaces of Riemannian metrics with specific curvature bounds on high-dimensional Spin-manifolds.
result Spaces of metrics with positive p-curvature and k-positive Ricci curvature have non-trivial homotopy groups.
Proves metrics with positive intermediate Ricci curvature on complex manifolds.
problem Establishing metrics with positive intermediate Ricci curvature on complex manifolds.
method Canonical variation and surgery techniques.
result Existence of metrics with positive intermediate Ricci curvature on various examples.
Extends Perelman's theorem to positive intermediate curvature conditions.
problem Positive intermediate curvature conditions and their implications.
method Generalization of Perelman's gluing theorem to positive intermediate curvature conditions.
result Observer moduli space can have non-trivial higher homotopy groups.
The study proves that certain manifolds with boundary cannot have metrics with positive intermediate curvatures.
problem Proving the nonexistence of metrics with positive intermediate curvatures on manifolds with boundary.
method Curvature obstruction theorems for manifolds with boundary.
result Topologically nontrivial compact manifolds with boundary cannot have metrics of positive m m m -intermediate curvature if the boundary is m m m -convex. We study the regularized determinant of the Laplacian as a functional on the space of Mandelstam diagrams (noncompact translation surfaces glued from finite and semi-infinite cylinders). A Mandelstam diagram can be considered as a compact Riemann surface equipped with a conformal flat singular metric ∣ ω ∣ 2 |ω|^2 ∣ ω ∣ 2 , where ω ω ω …
LIT compresses deep networks by training intermediate representations, outperforming traditional methods.
problem Reducing the computational overhead of deep network inference.
method LIT trains a student model with the same width but shallower depth, using the intermediate representations from the teacher model.
result LIT achieves substantial network depth reductions without accuracy loss, outperforming traditional methods.
Study finds metrics with positive intermediate Ricci curvature on specific low-dimensional manifolds.
problem Existence of invariant metrics with positive intermediate Ricci curvature on low-dimensional cohomogeneity one manifolds.
method Construction of invariant metrics with positive intermediate Ricci curvature on specific manifolds.
result Invariant metrics with positive 4th-intermediate Ricci curvature exist but not for 3rd-intermediate Ricci curvature on certain manifolds.
Symmetry rank bound for manifolds with positive intermediate Ricci curvature.
problem Bounding the symmetry rank of manifolds with positive intermediate Ricci curvature.
method Local argument and effective isometric action on manifolds.
result Symmetry rank bound r ≤ ⌊ n + k 2 f l o o r r \leq \lfloor \frac{n+k}{2}
floor r ≤ ⌊ 2 n + k f l oor for positive intermediate Ricci curvature. Sharp dimension constraints for positive intermediate curvature metrics are established.
problem Proving sharp dimension constraints for metrics with positive intermediate curvature.
method Constructing counterexamples and extending rigidity results.
result Sharp dimension constraints for positive intermediate curvature metrics are established.
This paper introduces a novel approach to measuring privacy risks in deep computer vision models based on intermediate outputs.
problem The exposure of intermediate results in hidden layers of deep computer vision models poses significant privacy concerns.
method The approach leverages Degrees of Freedom (DoF) to evaluate the amount of information retained in each layer and combines this with the rank of the Jacobian matrix to assess sensitivity to input variations.
result The proposed framework provides deeper insights into privacy risks associated with intermediate representations without requiring adversarial attack simulations.
The paper proves manifold splitting theorems with nonnegative intermediate curvature.
problem Proving rigidity results for manifolds with nonnegative intermediate curvatures.
method New recursion theorem for spectral intermediate curvatures and cylindrical splitting theorems.
result Smooth metrics with uniformly positive intermediate curvature constructed.
A framework to explain decoder-only sequence classification models using intermediate predictions.
problem Explaining predictions of decoder-only sequence classification models.
method Progressive Inference framework with Single Pass-Progressive Inference and Multi Pass-Progressive Inference methods.
result Significantly better attributions compared to prior work on text classification tasks.
Polyhedral semantics for intermediate logics; Nerve Criterion ensures completeness.
problem Characterize polyhedrally-complete intermediate logics.
method Developed Nerve Criterion to characterize polyhedrally-complete logics combinatorially.
result Nerve Criterion provides a necessary and sufficient condition for polyhedrally-completeness.
Classifies 2D TQFTs for orientable cobordisms using additional data.
problem Classifying 2D TQFTs for orientable cobordisms.
method Describes an intermediate framework using an involution and Möbius strip value.
result Intermediate classification of 2D TQFTs for orientable cobordisms.
We study rerouting edges on surfaces without crossings.
problem Reconfiguring edge paths on surfaces without crossing.
method Rerouting one edge at a time, maintaining crossing-free intermediate embeddings.
result Reconfiguration is always possible on the torus and any orientable surface of genus at least one.
A cost-effective framework for gradual domain adaptation using multifidelity.
problem Degrading prediction performance due to large domain distance.
method Combines multifidelity and active domain adaptation.
result Improves prediction performance with reduced sample cost.
The paper models asset prices using Wiener chaos expansions for efficient calibration to implied volatility surfaces.
problem Calibrating to implied volatility surfaces using flexible martingale models.
method Constructing an over-parameterized martingale model based on Wiener chaos expansions and conditional expectations.
result The method enables fast calibration to implied volatility surfaces and demonstrates flexibility through numerical experiments.
Gradual domain adaptation improves model transfer between domains with intermediate training.
problem Challenges in unsupervised domain adaptation when distribution shifts are large.
method Gradual self-training using intermediate domains along the Wasserstein geodesic.
result GOAT framework generates intermediate domains for improved adaptation.
Study shows Gromov's Betti number bound fails for certain intermediate Ricci curvatures.
problem Gromov's Betti number bound for sectional curvature bounded below does not hold for intermediate Ricci curvatures.
method Established a surgery result for Riemannian metrics with R i c k > 0 Ric_k>0 R i c k > 0 and showed failure of Gromov's bound for specific ranges of k k k . result Gromov's Betti number bound fails for R i c k > 0 Ric_k>0 R i c k > 0 when ⌊ n / 2 f l o o r + 2 ≤ k ≤ n − 1 \lfloor n/2
floor+2 \le k \le n-1 ⌊ n /2 f l oor + 2 ≤ k ≤ n − 1 . Study analyzes financial intermediation costs in decentralized lending protocols.
problem Understanding the cost of financial intermediation in decentralized lending protocols.
method Analysis of publicly available data on rates, supply, borrow activity, and accounts.
result Ex-post margins are 1% and lower for stablecoin markets.
Improved U-Nets with various intermediate blocks enhance singing voice separation.
problem Improving singing voice separation accuracy using U-Net architectures.
method Implemented and compared U-Nets with different intermediate spectrogram transformation blocks.
result A specific block type achieves state-of-the-art SDR by 0.9 dB.
Intermediate logic of all convex polyhedra is axiomatized.
problem Defining and axiomatizing intermediate logic for convex polyhedra.
method Using Jankov-Fine formulas, classical polyhedral geometry, and p-morphic images to establish completeness.
result A finite axiomatisation of PL for all convex polyhedra.
Study on Lee classes of complex surfaces, proving connectedness and bounds.
problem Understanding Lee classes of complex surfaces with LCS structures.
method Analyzing deRham classes of Lee 1-forms and using properties of PSH functions.
result Connectedness of Lee deRham classes and explicit negative upper bound on hyperbolic Kato surfaces.
We construct closed embedded minimal surfaces in the round three-sphere, resembling two parallel copies of the equatorial two-sphere, joined by small catenoidal bridges symmetrically arranged either along two parallel circles of the equator, or along the equatorial circle and the poles. To carry out these constructions…