Given H∈ [0,1) and given a C^0 exterior domain Ω in a H- hypersphere of ℍ^n+1, the existence of hyperbolic Killing graphs of CMC H defined in Ω with boundary ∂Ω included in the H- hypersphere is obtained.
We prove that a normal hyperplane section of the Segre variety Σ _m, n has a non-reductive automorphism group if m n or it is not smooth. In the smooth case, this recovers Hano’s result. Our proof proceeds at the level of Lie algebras.
Abstract We give a formula for a birational map on the Schubert cell associated to each Weyl group element of $$G=\operatorname {GL}(r)$$ G = GL ( r ) . The map simplifies the UDL decomposition of matrices, providing structural insight into the Schubert cell decomposition of the flag variety G / B , where B is a Borel subgroup. An application of the formula includes a new proof of the existence of Whittaker functionals for principal series representations of $$\operatorname {GL}(r,{\mathbb {R}})$$ GL ( r , R ) via integration by parts. In this paper, we establish combinatorial properties of the birational map and prove auxiliary results.
Let S_k denote the space of cusp forms of weight k and level one. We show that if k≫ n^2 then the first n odd or even periods are linearly independent on S_k . We also obtain a similar result for the symmetric square periods of modular forms.
We introduce an iterative scheme to solve the Yamabe equation - aΔ _g u + S u = λ u^p-1 on small domains Ω inside a compact Riemannian manifold (M, g). Thus g admits a conformal change to a constant scalar curvature metric. The proof does not use the traditional functional minimization.
We study $$\eta $$ η -Einstein Sasakian structures on Lie algebras, that is, Sasakian structures whose associated Ricci tensor satisfies an Einstein-like condition. We divide into the cases in which the Lie algebra’s centre is non-trivial (and necessarily one-dimensional) from those where it is zero. In the former case we show that any Sasakian structure on a unimodular Lie algebra is $$\eta $$ η -Einstein. As for centreless Sasakian Lie algebras, we devise a complete characterisation under certain dimensional assumptions regarding the action of the Reeb vector. Using this result, together with the theory of normal j -algebras and modifications of Hermitian Lie algebras, we construct new examples of $$\eta $$ η -Einstein Sasakian Lie algebras and solvmanifolds, and provide effective restrictions for their existence.
We generalize the centered and uncentered Hardy-Littlewood maximal function in terms of shape of integration sets. Continuity of two global and two local generalized maximal functions in R^n is studied. The global ones are continuous. One of the local ones is continuous, provided the integration set is star-shaped with respect to its center. For the second local one, we construct a counterexample.
In this paper we show how to replace hyperbolic cusps of a constant scalar curvature manifold with ends of infinite volume - funnels - keeping the scalar curvature constant and negative. This construction produces stable minimal tori belonging to a constant mean curvature foliation extending up to infinity. We discuss the relation of this construction with Penrose-type inequalities on time-symmetric relativistic initial data.
A strong version of the Beauville–Voisin conjecture asserts that for hyper-Kähler varieties, the subring of the Chow ring generated by divisors, Chern classes and Lagrangian constant cycle subvarieties should inject into cohomology. We verify this in codimension larger than two for Hilbert squares of K3 surfaces, for Fano varieties of lines in cubic fourfolds, and for double EPW sextics.
We prove, under a natural semisimplicity hypothesis, the equivariant Tamagawa number conjecture for log F-crystals over finite unramified Galois extensions of varieties over finite fields of characteristic p>0 .
In this paper we study an extension of maximal Calderón–Zygmund type singular integral T_β^*f (x) =sup _ε >0 |∫ _|y|≥εΩ (y)/|y|^n-βf(x-y)dy | and non-tangential maximal Calderón–Zygmund type singular integral T_Γ _α,β^* f(x):= sup _(y,ε )∈Γ _α(x) |∫ _|t|≥εΩ (t)/|t|^n-βf(y-t)dt |, where Γ _α(x)={(y,ε )∈ℝ^n× (0,∞ ): |x-y|<αε} and α >0 is fixed. We establish the uniform L^q estimate ( 1
In this paper, we study surfaces z=φ (x,y) in Euclidean space that satisfy the equation φ _xx+φ _yy=Λ/2 where Λ∈ℝ is a real constant. We classify these surfaces when they are the zero level sets of an implicit equation of the type f(x)+g(y)+h(z)=0 , where f, g and h are smooth functions of one variable. If Λ =0 , we find a large family of surfaces with interesting symmetry properties. However, if Λ≠0 , we show that the surfaces must be either surfaces of revolution or of the type z=f(x)+g(y) ; furthermore, explicit parametrizations of these surfaces are obtained.
In this paper, we show that if a K-trivial threefold has singularities worse than canonical singularities or its singular locus is one-dimensional, then a strictly nef divisor on it is ample. We also investigate the strictly nefness on K-trivial threefolds with isolated canonical singularities.
Our purpose is to investigate geometric aspects of complete and stochastically complete CMC spacelike hypersurfaces immersed into a class of Lorentzian Einstein manifolds satisfying appropriate curvature constraints. Assuming that the total umbilicity tensor satisfies an Okumura type inequality, we derive a suitable Simons type inequality which, jointly with several maximum principles and certain integrability conditions, enable us to establish rigidity and nonexistence results concerning these spacelike hypersurfaces.
We construct moduli spaces of G-equivariant harmonic maps between spheres, where G is a subgroup of the orthogonal group. For G=SU(m) , U(m) , Sp(m) , Sp(m)×U(1) or Sp(m)×Sp(1) , we obtain identity theorems: (i) The restriction to S^5 of any SU(m) -equivariant harmonic map of S^2m-1 is SU(3) -equivariant and harmonic. (ii) Any SU(3) -equivariant harmonic map of S^5 can be uniquely extended to an SU(m) -equivariant harmonic map of S^2m-1 . For the other groups, we have similar results.
