Displaying similar documents to “How to define 'convex functions' on differentiable manifolds”

Foliated structure of the Kuranishi space and isomorphisms of deformation families of compact complex manifolds

Laurent Meersseman (2011)

Annales scientifiques de l'École Normale Supérieure

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Consider the following uniformization problem. Take two holomorphic (parametrized by some analytic set defined on a neighborhood of 0 in p , for some p > 0 ) or differentiable (parametrized by an open neighborhood of 0 in p , for some p > 0 ) deformation families of compact complex manifolds. Assume they are pointwise isomorphic, that is for each point t of the parameter space, the fiber over t of the first family is biholomorphic to the fiber over t of the second family. Then, under which conditions...

Exotic Deformations of Calabi-Yau Manifolds

Paolo de Bartolomeis, Adriano Tomassini (2013)

Annales de l’institut Fourier

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We introduce Quantum Inner State manifolds (QIS manifolds) as (compact) 2 n -dimensional symplectic manifolds ( M , κ ) endowed with a κ -tamed almost complex structure J and with a nowhere vanishing and normalized section ϵ of the bundle Λ J n , 0 ( M ) satisfying the condition ¯ J ϵ = 0 . We study the moduli space 𝔐 of QIS deformations of a given Calabi-Yau manifold, computing its tangent space...

Finiteness problems on Nash manifolds and Nash sets

José F. Fernando, José Manuel Gamboa, Jesús M. Ruiz (2014)

Journal of the European Mathematical Society

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We study here several finiteness problems concerning affine Nash manifolds M and Nash subsets X . Three main results are: (i) A Nash function on a semialgebraic subset Z of M has a Nash extension to an open semialgebraic neighborhood of Z in M , (ii) A Nash set X that has only normal crossings in M can be covered by finitely many open semialgebraic sets U equipped with Nash diffeomorphisms ( u 1 , , u m ) : U m such that U X = { u 1 u r = 0 } , (iii) Every affine Nash manifold with corners N is a closed subset of an affine Nash...

Z k -actions with a special fixed point set

Pedro L. Q. Pergher, Rogério de Oliveira (2005)

Fundamenta Mathematicae

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Let Fⁿ be a connected, smooth and closed n-dimensional manifold satisfying the following property: if N m is any smooth and closed m-dimensional manifold with m > n and T : N m N m is a smooth involution whose fixed point set is Fⁿ, then m = 2n. We describe the equivariant cobordism classification of smooth actions ( M m ; Φ ) of the group G = Z k on closed smooth m-dimensional manifolds M m for which the fixed point set of the action is a submanifold Fⁿ with the above property. This generalizes a result of F....

Complex structures on product of circle bundles over complex manifolds

Parameswaran Sankaran, Ajay Singh Thakur (2013)

Annales de l’institut Fourier

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Let L ¯ i X i be a holomorphic line bundle over a compact complex manifold for i = 1 , 2 . Let S i denote the associated principal circle-bundle with respect to some hermitian inner product on L ¯ i . We construct complex structures on S = S 1 × S 2 which we refer to as scalar, diagonal, and linear types. While scalar type structures always exist, the more general diagonal but non-scalar type structures are constructed assuming that L ¯ i are equivariant ( * ) n i -bundles satisfying some additional conditions....

The natural operators T | f T * T r * and T | f Λ ² T * T r *

W. M. Mikulski (2002)

Colloquium Mathematicae

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Let r and n be natural numbers. For n ≥ 2 all natural operators T | f T * T r * transforming vector fields on n-manifolds M to 1-forms on T r * M = J r ( M , ) are classified. For n ≥ 3 all natural operators T | f Λ ² T * T r * transforming vector fields on n-manifolds M to 2-forms on T r * M are completely described.

An extension of Mazur's theorem on Gateaux differentiability to the class of strongly α (·)-paraconvex functions

S. Rolewicz (2006)

Studia Mathematica

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Let (X,||·||) be a separable real Banach space. Let f be a real-valued strongly α(·)-paraconvex function defined on an open convex subset Ω ⊂ X, i.e. such that f ( t x + ( 1 - t ) y ) t f ( x ) + ( 1 - t ) f ( y ) + m i n [ t , ( 1 - t ) ] α ( | | x - y | | ) . Then there is a dense G δ -set A G Ω such that f is Gateaux differentiable at every point of A G .

η -Ricci Solitons on η -Einstein ( L C S ) n -Manifolds

Shyamal Kumar Hui, Debabrata Chakraborty (2016)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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The object of the present paper is to study η -Ricci solitons on η -Einstein ( L C S ) n -manifolds. It is shown that if ξ is a recurrent torse forming η -Ricci soliton on an η -Einstein ( L C S ) n -manifold then ξ is (i) concurrent and (ii) Killing vector field.

On almost complex structures from classical linear connections

Jan Kurek, Włodzimierz M. Mikulski (2017)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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Let f m be the category of m -dimensional manifolds and local diffeomorphisms and  let T be the tangent functor on f m . Let 𝒱 be the category of real vector spaces and linear maps and let 𝒱 m be the category of m -dimensional real vector spaces and linear isomorphisms. We characterize all regular covariant functors F : 𝒱 m 𝒱 admitting f m -natural operators J ˜ transforming classical linear connections on m -dimensional manifolds M into almost complex structures J ˜ ( ) on F ( T ) M = x M F ( T x M ) .

Local density of diffeomorphisms with large centralizers

Christian Bonatti, Sylvain Crovisier, Gioia M. Vago, Amie Wilkinson (2008)

Annales scientifiques de l'École Normale Supérieure

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Given any compact manifold M , we construct a non-empty open subset 𝒪 of the space Diff 1 ( M ) of C 1 -diffeomorphisms and a dense subset 𝒟 𝒪 such that the centralizer of every diffeomorphism in 𝒟 is uncountable, hence non-trivial.

Canonical contact forms on spherical CR manifolds

Wei Wang (2003)

Journal of the European Mathematical Society

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We construct the CR invariant canonical contact form can ( J ) on scalar positive spherical CR manifold ( M , J ) , which is the CR analogue of canonical metric on locally conformally flat manifold constructed by Habermann and Jost. We also construct another canonical contact form on the Kleinian manifold Ω ( Γ ) / Γ , where Γ is a convex cocompact subgroup of Aut C R S 2 n + 1 = P U ( n + 1 , 1 ) and Ω ( Γ ) is the discontinuity domain of Γ . This contact form can be used to prove that Ω ( Γ ) / Γ is scalar positive (respectively, scalar negative, or scalar vanishing)...

The L 2 ¯ -Cauchy problem on weakly q -pseudoconvex domains in Stein manifolds

Sayed Saber (2015)

Czechoslovak Mathematical Journal

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Let X be a Stein manifold of complex dimension n 2 and Ω X be a relatively compact domain with C 2 smooth boundary in X . Assume that Ω is a weakly q -pseudoconvex domain in X . The purpose of this paper is to establish sufficient conditions for the closed range of ¯ on Ω . Moreover, we study the ¯ -problem on Ω . Specifically, we use the modified weight function method to study the weighted ¯ -problem with exact support in Ω . Our method relies on the L 2 -estimates by Hörmander (1965) and by Kohn (1973). ...

On the Configuration Spaces of Grassmannian Manifolds

Sandro Manfredini, Simona Settepanella (2014)

Annales de la faculté des sciences de Toulouse Mathématiques

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Let h i ( k , n ) be the i -th ordered configuration space of all distinct points H 1 , ... , H h in the Grassmannian G r ( k , n ) of k -dimensional subspaces of n , whose sum is a subspace of dimension i . We prove that h i ( k , n ) is (when non empty) a complex submanifold of G r ( k , n ) h of dimension i ( n - i ) + h k ( i - k ) and its fundamental group is trivial if i = m i n ( n , h k ) , h k n and n > 2 and equal to the braid group of the sphere P 1 if n = 2 . Eventually we compute the fundamental group in the special case of hyperplane arrangements, i.e. k = n - 1 .

On the Picard number of divisors in Fano manifolds

Cinzia Casagrande (2012)

Annales scientifiques de l'École Normale Supérieure

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Let  X be a complex Fano manifold of arbitrary dimension, and D a prime divisor in  X . We consider the image 𝒩 1 ( D , X ) of  𝒩 1 ( D ) in  𝒩 1 ( X ) under the natural push-forward of 1 -cycles. We show that ρ X - ρ D codim 𝒩 1 ( D , X ) 8 . Moreover if codim 𝒩 1 ( D , X ) 3 , then either X S × T where S is a Del Pezzo surface, or codim 𝒩 1 ( D , X ) = 3 and X has a fibration in Del Pezzo surfaces onto a Fano manifold T such that ρ X - ρ T = 4 .

Notes on strongly Whyburn spaces

Masami Sakai (2016)

Commentationes Mathematicae Universitatis Carolinae

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We introduce the notion of a strongly Whyburn space, and show that a space X is strongly Whyburn if and only if X × ( ω + 1 ) is Whyburn. We also show that if X × Y is Whyburn for any Whyburn space Y , then X is discrete.

On lifts of projectable-projectable classical linear connections to the cotangent bundle

Anna Bednarska (2013)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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We describe all 2 m 1 , m 2 , n 1 , n 2 -natural operators D : Q p r o j - p r o j τ Q T * transforming projectable-projectable classical torsion-free linear connections on fibred-fibred manifolds Y into classical linear connections D ( ) on cotangent bundles T * Y of Y . We show that this problem can be reduced to finding 2 m 1 , m 2 , n 1 , n 2 -natural operators D : Q p r o j - p r o j τ ( T * , p T * q T ) for p = 2 , q = 1 and p = 3 , q = 0 .

On the Schröder equation

M. Kuczma

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CONTENTSPART IIntroduction............................................................................................... 31. General solution.................................................................................. 42. Preliminaries and notation................................................................ 53. C p solutions in *................................................ 74. Change of variables..............................................................................

Product property for capacities in N

Mirosław Baran, Leokadia Bialas-Ciez (2012)

Annales Polonici Mathematici

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The paper deals with logarithmic capacities, an important tool in pluripotential theory. We show that a class of capacities, which contains the L-capacity, has the following product property: C ν ( E × E ) = m i n ( C ν ( E ) , C ν ( E ) ) , where E j and ν j are respectively a compact set and a norm in N j (j = 1,2), and ν is a norm in N + N , ν = ν₁⊕ₚ ν₂ with some 1 ≤ p ≤ ∞. For a convex subset E of N , denote by C(E) the standard L-capacity and by ω E the minimal width of E, that is, the minimal Euclidean distance between two supporting hyperplanes...