New surfaces found in a special space.
problem Creating surfaces in a unique space.
method Constructed surfaces with specific properties.
result Found surfaces with mixed type and Schwarz rPD topology.
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
169,291 papers · 148 categories
Trend · papers per month
48 results for “Schwarz rPD surfaces”
Minimal Twin Surfacesmath.DG
Minimal twin surfaces are found in material science, resembling crystal twins.
problem Finding mathematical and physical existence of twin surfaces.
method Employed Brakke's Surface Evolver to construct and analyze minimal twin surfaces.
result Strong evidence for the existence of D and G twins, and new cubic polyhedral models for G twins.
Paper extends RPD for better handling multiple modalities and non-convexity.
problem Handling multiple modalities and non-convexity in data clouds.
method Computes RPD in a reproducing kernel Hilbert space using kernel principal component analysis.
result The method outperforms RPD and is comparable to other models on benchmark datasets.
Higher dimensional generalizations of Schwarz's -surface, Schwarz's -surface and Scherk's second surface are constructed as complete embedded periodic minimal hy- persurfaces in .
Proof of Schwarz principle for specific minimal surfaces.
problem Reflection principle for Jenkins-Serrin type minimal surfaces.
method Proof in homogeneous three-manifolds for κ≤0 and τ≥0.
result Verification of Schwarz reflection principle for new class of minimal surfaces.
New 2-parameter family of triply periodic minimal surfaces, sharing properties with Schwarz' D but distinct.
problem Proving the existence of a new family of triply periodic minimal surfaces.
method Proved existence through mathematical proof and analysis of properties.
result New family o does not belong to Meeks' five-dimensional family but shares properties with Schwarz' D.
We use bifurcation theory to determine the existence of infinitely many new examples of triply periodic minimal surfaces in . These new examples form branches issuing from the H-family, the rPD-family, the tP-family, and the tD-family, that converge to some degenerate embedding of the families. As to nonde…
The paper creates symmetrical discrete minimal nets using Schwarz reflection.
problem Creating symmetrical discrete minimal nets.
method Extending Schwarz reflection principle to discrete minimal surfaces.
result Global examples of discrete minimal nets with high symmetry.
Schwarz H surfaces can be continuously deformed into Meeks surfaces.
problem Classifying and understanding the relationship between Schwarz H surfaces and Meeks surfaces.
method Constructing a 2-parameter family of TPMS of genus three that contains both H and Meeks surfaces.
result Schwarz H surfaces can be continuously deformed into Meeks surfaces.
Minimal maps on curved surfaces decrease area.
problem Understanding area behavior of minimal maps on curved surfaces.
method Proved a Schwarz-Pick lemma for minimal maps between negatively curved Riemannian surfaces.
result Minimal maps between negatively curved Riemannian surfaces are area decreasing.
New embedded periodic surfaces constructed in n-dimensional space.
problem Constructing new types of minimal surfaces in higher dimensions.
method Starting with a Jordan curve, a Plateau minimal disk is formed and extended using Schwarz reflections to create an embedded surface.
result Characterization of Jordan curves that generate embedded surfaces in n-dimensional space.
Residual Prior Diffusion integrates coarse latent priors with diffusion models for better generative tasks.
problem Diffusion models struggle with representing both large-scale and fine-scale details in data distributions.
method Two-stage framework: first a coarse prior model captures large-scale structure, then a diffusion model represents the residual.
result RPD accurately captures fine-scale details while preserving large-scale structure, outperforming standard diffusion models.
Through the Schwarz lemma, we provide a new point of view on three well-known results of the geometry of hyperbolic surfaces. The first result deal with the length of closed geodesics on hyperbolic surfaces with boundary (Thurston, Parlier, Papadopoulos-Théret). The two others give sharp lower bounds on two metric inva…
We study the injectivity radius of complete Riemannian surfaces (S,g) with curvature |K(g)| bounded by 1. We show that if S is orientable with nonabelian fundamental group, then there is a point p in S with injectivity radius at least arcsinh(2/\sqrt{3}). This lower bound is sharp independently of the topology of S. Th…
We study Dirac-harmonic maps from degenerating spin surfaces with uniformly bounded energy and show the so-called generalized energy identity in the case that the domain converges to a spin surface with only Neveu-Schwarz type nodes. We find condition that is both necessary and sufficient for the …
Study relaxed curvature for surfaces, focusing on energy and BV properties.
problem Defining curvature for non-parametric surfaces with BV and measure properties.
method Examined inscribed polyhedral surfaces to approximate relaxed energy, analyzed BV properties and total curvature.
result Properties of functions with finite relaxed energy, analyzed Schwarz-Peano counterexample.
Sharp estimate on harmonic maps at conformal points in balls.
problem Estimating harmonic maps at conformal points in balls.
method Sharp estimate on differential norm using Schwarz-Pick lemma.
result Generalizes classical Schwarz-Pick lemma and gives optimal for .
Let be a homeomorphism between hyperbolic surfaces with finite topology. If is homotopic to a holomorphic map, then every closed geodesic in is at least as long as the corresponding geodesic in , by the Schwarz Lemma. The converse holds trivially when and are disks or annuli, and it holds…
Paper estimates Gaussian curvature of minimal graphs in a specific manifold.
problem Estimating Gaussian curvature of minimal graphs in .
method Using Weierstrass representation via harmonic mappings and Schwarz lemma type results.
result Proves Schwarz lemma type and Heinz type results for harmonic mappings.
A super-conformal map and a minimal surface are factored into a product of two maps by modeling the Euclidean four-space and the complex Euclidean plane on the set of all quaternions. One of these two maps is a holomorphic map or a meromorphic map. These conformal maps adopt properties of a holomorphic function or a me…
Embedded triply periodic zero mean curvature surfaces of mixed type in Lorentz-Minkowski 3-spacemath.DG
We construct embedded triply periodic zero mean curvature surfaces of mixed type in the Lorentz-Minkowski 3-space with the same topology as the Schwarz D surface in the Euclidean 3-space.
The paper calculates Morse indices and nullities for triply periodic minimal surfaces.
problem Computing Morse indices and nullities for triply periodic minimal surfaces.
method Developed an algorithm to compute Morse index and nullity using matrix properties of abelian differentials.
result Explicitly determined key matrices for five families of triply periodic minimal surfaces.
The paper constructs free boundary minimal surfaces in product spaces using eigenvalue methods.
problem Constructing free boundary minimal surfaces in product spaces of balls.
method Extremal eigenvalue approach involving mixed Steklov-Neumann eigenvalues.
result No absolute maximum exists for the problem in product spaces.
We give a uniform and elementary treatment of many classical and new triply periodic minimal surfaces in Euclidean space, based on a Schwarz-Christoffel formula for periodic polygons in the plane. Our surfaces share the property that vertical symmetry planes cut them into simply connected pieces.
The article approximates solutions to the Beltrami equation using similarity surfaces.
problem Approximating solutions to the Beltrami equation.
method Constructing similarity surfaces from polygons and analyzing their conformal uniformization.
result Holomorphic dependence of Christoffel symbols on polygons and convergence to a specific affine connection.
New Schwarz Lemma for Bergman metrics in bounded domains.
problem Finding bounds for Bergman metrics in bounded domains.
method Using Cauchy-Schwarz inequality from probability theory.
result Established a new Schwarz Lemma for Bergman metrics.
Explains the Schwarz lemma in lecture notes.
problem None explicitly stated; focuses on explanation.
method Expository notes on the Schwarz lemma.
result Explains the Schwarz lemma.
A new slicing method speeds up sliced Wasserstein estimation.
problem Efficiently estimating sliced Wasserstein distance.
method Random-Path Projecting Direction (RPD) for fast sampling.
result RPSW and IWRPSW show favorable performance in training generative models.
The paper solves circle packings on surfaces with boundaries.
problem Circle packing on surfaces with boundaries and finite genus.
method Using Thurston's algorithm and discrete Schwarz-Pick lemma.
result A unique solution to the boundary value problem exists.
The paper extends Schwarz's lemma to RC-positivity and complex manifolds.
problem Comparing metrics with RC-positivity in complex manifolds.
method Establishing Schwarz lemmas for RC-positivity and applying them to complex manifolds.
result New diameter and volume comparison theorems.
Unified Schwarz lemma in Kähler and Hermitian geometry.
problem Various forms of the Schwarz lemma in Kähler and Hermitian geometry.
method Introducing new curvatures to refine and elucidate the real bisectional curvature.
result Unified Chern-Lu, Aubin-Yau, and Chen-Cheng-Look Schwarz lemmas.
Paper generalizes Schwarz Lemma for VT harmonic maps with conditions.
problem Generalizing Schwarz Lemma for a specific type of harmonic maps.
method Conditions on eigenvalues and Ricci curvature are used to prove the lemma.
result Schwarz Lemma for VT harmonic maps proved with distance and volume decreasing properties.
Schwarz lemma extended to equality cases and curvature on manifolds.
problem Extending Schwarz lemma to equality cases and studying curvature.
method Analyzing Schwarz lemma inequalities and equalities, studying holomorphic sectional curvature.
result Holomorphic maps are totally geodesic and have constant rank when Schwarz lemma equality holds.
Paper introduces capillary Schwarz symmetrization in half-space.
problem Capillary problems in half-space.
method Introduces a special anisotropic gauge to transform capillary symmetrization to convex symmetrization.
result Capillary Schwarz symmetrization in half-space established.
We prove that closed surfaces of all topological types, except for the non-orientable odd-genus ones, can be minimally embedded in the Riemannian product of a sphere and a circle of arbitrary radius. We illustrate it by obtaining some periodic minimal surfaces in via conjugate constructio…
Boundary Value Problem and Discrete Schwarz-Pick Lemma for Generalized Hyperbolic Circle Packingsmath.DG
Paper proves a discrete Schwarz-Pick lemma for generalized circle packings.
problem Comparing geometric quantities of circle packings with different boundary values.
method Combinatorial Calabi flows and maximum principle.
result Discrete Schwarz-Pick lemma proven for generalized circle packings.
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.
In this paper, we prove the existence and uniqueness theorem for parabolic conical metrics on Riemann surfaces in the situation of generalized real angles, positive, zero and negative, by complex analysis, and give an example of this theorem to clarify concrete expressions of parabolic metrics on the two-sphere and gen…
Paper generalizes Schwarz lemma for harmonic maps between Riemannian manifolds.
problem Generalizing Schwarz lemma for harmonic maps.
method Using Bochner techniques and sub-Laplacian comparison theorem.
result Established a generalization of Schwarz lemma for transversally harmonic maps.
Proves new Schwarz Lemmata for Kähler manifolds.
problem Geometric aspects of Kähler manifolds with specific curvature conditions.
method Proves estimates interpolating existing Schwarz Lemmata.
result Provides additional geometric information on Kähler manifolds.
New results on geometry of area-preserving diffeomorphisms using braids.
problem Large-scale geometry of area-preserving diffeomorphisms on surfaces.
method Application of Schwarz-Milnor lemma to configuration spaces.
result Quasi-isometric embeddings and Lipschitz properties of quasi-morphisms.
Enhanced Schwarz lemma for Hermitian manifolds with new curvature constraints.
problem Improving Schwarz lemma for holomorphic maps between Hermitian manifolds.
method Introducing new curvature constraints on source and target manifolds, controlling by holomorphic sectional curvature.
result Significant improvements on the Wu--Yau theorem and Schwarz lemma for Gauduchon connections.
Generalizes Schwarz lemma for conical Kähler metrics with arbitrary cone angles.
problem Applying Schwarz lemma to conical Kähler metrics with general cone angles.
method Using a barrier function and maximum principle argument, extending to arbitrary cone angles.
result Generalized Schwarz lemma to conical Kähler metrics with arbitrary cone angles.
This paper is about interpolating minimal surfaces between two real analytic curves, a and b, each of which are simple real analytic curves, using the Björling-Schwarz formula in the domain where it is valid, changing the normal distributions on inital curves. We insert curves at specific locations and cla…
Two new boundary Schwarz lemmas for holomorphic maps established.
problem Establishing boundary Schwarz lemmas for holomorphic maps.
method Two boundary versions of the Schwarz lemma for holomorphic maps.
result First boundary Schwarz lemmas for general holomorphic self maps and biholomorphisms with invariant Kähler metrics.
Abstract: Generalizes Milnor-Schwarz lemma to inverse monoids.
problem Applying Milnor-Schwarz lemma to inverse monoids.
method Two proofs provided: elementary and using Vietoris-Rips complex.
result Generalization of Milnor-Schwarz lemma to inverse monoids.
Paper calculates eigenvalues of a specific triangle on a sphere.
problem Computing eigenvalues of a specific triangle on a sphere.
method Computed first two Dirichlet eigenvalues and eigenfunctions of the equilateral Schwarz triangle (3/2 3/2 3/2) on the sphere.
result Computed the first two Dirichlet eigenvalues and eigenfunctions of the equilateral Schwarz triangle (3/2 3/2 3/2).
The paper establishes Schwarz type lemmas for holomorphic maps between pseudo-Hermitian and Hermitian manifolds.
problem Analyzing holomorphic maps between pseudo-Hermitian and Hermitian manifolds.
method Using Bochner formulas and comparison theorems.
result Established Schwarz type lemmas for holomorphic maps.