Displaying similar documents to “Conformal Killing graphs in foliated Riemannian spaces with density: rigidity and stability”

Conformal harmonic forms, Branson–Gover operators and Dirichlet problem at infinity

Erwann Aubry, Colin Guillarmou (2011)

Journal of the European Mathematical Society

Similarity:

For odd-dimensional Poincaré–Einstein manifolds ( X n + 1 , g ) , we study the set of harmonic k -forms (for k < n / 2 ) which are C m (with m ) on the conformal compactification X ¯ of X . This set is infinite-dimensional for small m but it becomes finite-dimensional if m is large enough, and in one-to-one correspondence with the direct sum of the relative cohomology H k ( X ¯ , X ¯ ) and the kernel of the Branson–Gover [3] differential operators ( L k , G k ) on the conformal infinity ( X ¯ , [ h 0 ] ) . We also relate the set of C n - 2 k + 1 ( Λ k ( X ¯ ) ) forms in the kernel of d + δ g ...

The almost Einstein operator for ( 2 , 3 , 5 ) distributions

Katja Sagerschnig, Travis Willse (2017)

Archivum Mathematicum

Similarity:

For the geometry of oriented ( 2 , 3 , 5 ) distributions ( M , ) , which correspond to regular, normal parabolic geometries of type ( G 2 , P ) for a particular parabolic subgroup P < G 2 , we develop the corresponding tractor calculus and use it to analyze the first BGG operator Θ 0 associated to the 7 -dimensional irreducible representation of G 2 . We give an explicit formula for the normal connection on the corresponding tractor bundle and use it to derive explicit expressions for this operator. We also show that solutions...

Edit distance measure for graphs

Tomasz Dzido, Krzysztof Krzywdziński (2015)

Czechoslovak Mathematical Journal

Similarity:

In this paper, we investigate a measure of similarity of graphs similar to the Ramsey number. We present values and bounds for g ( n , l ) , the biggest number k guaranteeing that there exist l graphs on n vertices, each two having edit distance at least k . By edit distance of two graphs G , F we mean the number of edges needed to be added to or deleted from graph G to obtain graph F . This new extremal number g ( n , l ) is closely linked to the edit distance of graphs. Using probabilistic methods we show...

On the multiplicity of eigenvalues of conformally covariant operators

Yaiza Canzani (2014)

Annales de l’institut Fourier

Similarity:

Let ( M , g ) be a compact Riemannian manifold and P g an elliptic, formally self-adjoint, conformally covariant operator of order m acting on smooth sections of a bundle over M . We prove that if P g has no rigid eigenspaces (see Definition 2.2), the set of functions f C ( M , ) for which P e f g has only simple non-zero eigenvalues is a residual set in C ( M , ) . As a consequence we prove that if P g has no rigid eigenspaces for a dense set of metrics, then all non-zero eigenvalues are simple for a residual set of metrics...

Mobius invariant Besov spaces on the unit ball of n

Małgorzata Michalska, Maria Nowak, Paweł Sobolewski (2011)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

Similarity:

We give new characterizations of the analytic Besov spaces B p on the unit ball 𝔹 of n in terms of oscillations and integral means over some Euclidian balls contained in 𝔹 .

The CR Yamabe conjecture the case n = 1

Najoua Gamara (2001)

Journal of the European Mathematical Society

Similarity:

Let ( M , θ ) be a compact CR manifold of dimension 2 n + 1 with a contact form θ , and L = ( 2 + 2 / n ) Δ b + R its associated CR conformal laplacien. The CR Yamabe conjecture states that there is a contact form θ ˜ on M conformal to θ which has a constant Webster curvature. This problem is equivalent to the existence of a function u such that L u = u 1 + 2 / n , u > 0 on M . D. Jerison and J. M. Lee solved the CR Yamabe problem in the case where n 2 and ( M , θ ) is not locally CR equivalent to the sphere S 2 n + 1 of 𝐂 n . In a join work with R. Yacoub, the CR Yamabe...

Note on a conjecture for the sum of signless Laplacian eigenvalues

Xiaodan Chen, Guoliang Hao, Dequan Jin, Jingjian Li (2018)

Czechoslovak Mathematical Journal

Similarity:

For a simple graph G on n vertices and an integer k with 1 k n , denote by 𝒮 k + ( G ) the sum of k largest signless Laplacian eigenvalues of G . It was conjectured that 𝒮 k + ( G ) e ( G ) + k + 1 2 , where e ( G ) is the number of edges of G . This conjecture has been proved to be true for all graphs when k { 1 , 2 , n - 1 , n } , and for trees, unicyclic graphs, bicyclic graphs and regular graphs (for all k ). In this note, this conjecture is proved to be true for all graphs when k = n - 2 , and for some new classes of graphs.

Intrinsic linking and knotting are arbitrarily complex

Erica Flapan, Blake Mellor, Ramin Naimi (2008)

Fundamenta Mathematicae

Similarity:

We show that, given any n and α, any embedding of any sufficiently large complete graph in ℝ³ contains an oriented link with components Q₁, ..., Qₙ such that for every i ≠ j, | l k ( Q i , Q j ) | α and | a ( Q i ) | α , where a ( Q i ) denotes the second coefficient of the Conway polynomial of Q i .

Embedding products of graphs into Euclidean spaces

Mikhail Skopenkov (2003)

Fundamenta Mathematicae

Similarity:

For any collection of graphs G , . . . , G N we find the minimal dimension d such that the product G × . . . × G N is embeddable into d (see Theorem 1 below). In particular, we prove that (K₅)ⁿ and ( K 3 , 3 ) are not embeddable into 2 n , where K₅ and K 3 , 3 are the Kuratowski graphs. This is a solution of a problem of Menger from 1929. The idea of the proof is a reduction to a problem from so-called Ramsey link theory: we show that any embedding L k O S 2 n - 1 , where O is a vertex of (K₅)ⁿ, has a pair of linked (n-1)-spheres.

Saturation numbers for linear forests P 6 + t P 2

Jingru Yan (2023)

Czechoslovak Mathematical Journal

Similarity:

A graph G is H -saturated if it contains no H as a subgraph, but does contain H after the addition of any edge in the complement of G . The saturation number, sat ( n , H ) , is the minimum number of edges of a graph in the set of all H -saturated graphs of order n . We determine the saturation number sat ( n , P 6 + t P 2 ) for n 10 3 t + 10 and characterize the extremal graphs for n > 10 3 t + 20 .

Note on improper coloring of 1 -planar graphs

Yanan Chu, Lei Sun, Jun Yue (2019)

Czechoslovak Mathematical Journal

Similarity:

A graph G = ( V , E ) is called improperly ( d 1 , , d k ) -colorable if the vertex set V can be partitioned into subsets V 1 , , V k such that the graph G [ V i ] induced by the vertices of V i has maximum degree at most d i for all 1 i k . In this paper, we mainly study the improper coloring of 1 -planar graphs and show that 1 -planar graphs with girth at least 7 are ( 2 , 0 , 0 , 0 ) -colorable.

1 -cocycles on the group of contactomorphisms on the supercircle S 1 | 3 generalizing the Schwarzian derivative

Boujemaa Agrebaoui, Raja Hattab (2016)

Czechoslovak Mathematical Journal

Similarity:

The relative cohomology H diff 1 ( 𝕂 ( 1 | 3 ) , 𝔬𝔰𝔭 ( 2 , 3 ) ; 𝒟 λ , μ ( S 1 | 3 ) ) of the contact Lie superalgebra 𝕂 ( 1 | 3 ) with coefficients in the space of differential operators 𝒟 λ , μ ( S 1 | 3 ) acting on tensor densities on S 1 | 3 , is calculated in N. Ben Fraj, I. Laraied, S. Omri (2013) and the generating 1 -cocycles are expressed in terms of the infinitesimal super-Schwarzian derivative 1 -cocycle s ( X f ) = D 1 D 2 D 3 ( f ) α 3 1 / 2 , X f 𝕂 ( 1 | 3 ) which is invariant with respect to the conformal subsuperalgebra 𝔬𝔰𝔭 ( 2 , 3 ) of 𝕂 ( 1 | 3 ) . In this work we study the supergroup case. We give an explicit construction of 1 -cocycles...

Universal Taylor series, conformal mappings and boundary behaviour

Stephen J. Gardiner (2014)

Annales de l’institut Fourier

Similarity:

A holomorphic function f on a simply connected domain Ω is said to possess a universal Taylor series about a point in Ω if the partial sums of that series approximate arbitrary polynomials on arbitrary compacta K outside Ω (provided only that K has connected complement). This paper shows that this property is not conformally invariant, and, in the case where Ω is the unit disc, that such functions have extreme angular boundary behaviour.

Maximum bipartite subgraphs in H -free graphs

Jing Lin (2022)

Czechoslovak Mathematical Journal

Similarity:

Given a graph G , let f ( G ) denote the maximum number of edges in a bipartite subgraph of G . Given a fixed graph H and a positive integer m , let f ( m , H ) denote the minimum possible cardinality of f ( G ) , as G ranges over all graphs on m edges that contain no copy of H . In this paper we prove that f ( m , θ k , s ) 1 2 m + Ω ( m ( 2 k + 1 ) / ( 2 k + 2 ) ) , which extends the results of N. Alon, M. Krivelevich, B. Sudakov. Write K k ' and K t , s ' for the subdivisions of K k and K t , s . We show that f ( m , K k ' ) 1 2 m + Ω ( m ( 5 k - 8 ) / ( 6 k - 10 ) ) and f ( m , K t , s ' ) 1 2 m + Ω ( m ( 5 t - 1 ) / ( 6 t - 2 ) ) , improving a result of Q. Zeng, J. Hou. We also give lower bounds on...

The real symmetric matrices of odd order with a P-set of maximum size

Zhibin Du, Carlos Martins da Fonseca (2016)

Czechoslovak Mathematical Journal

Similarity:

Suppose that A is a real symmetric matrix of order n . Denote by m A ( 0 ) the nullity of A . For a nonempty subset α of { 1 , 2 , ... , n } , let A ( α ) be the principal submatrix of A obtained from A by deleting the rows and columns indexed by α . When m A ( α ) ( 0 ) = m A ( 0 ) + | α | , we call α a P-set of A . It is known that every P-set of A contains at most n / 2 elements. The graphs of even order for which one can find a matrix attaining this bound are now completely characterized. However, the odd case turned out to be more difficult to tackle. As...