Displaying similar documents to “Concentrated monotone measures with non-unique tangential behavior in ℝ 3 ”

Monotone measures with bad tangential behavior in the plane

Robert Černý, Jan Kolář, Mirko Rokyta (2011)

Commentationes Mathematicae Universitatis Carolinae

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We show that for every ε > 0 , there is a set A ⊂ ℝ 2 such that ℋ 1 ⌞ A is a monotone measure, the corresponding tangent measures at the origin are not unique and ℋ 1 ⌞ A has the 1 -dimensional density between 1 and 3 + ε everywhere on the support.

Carleman estimates for a subelliptic operator and unique continuation

Nicola Garofalo, Zhongwei Shen (1994)

Annales de l'institut Fourier

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We establish a Carleman type inequality for the subelliptic operator ℒ = Δ z + | x | 2 ∂ t 2 in ℝ n + 1 , n ≥ 2 , where z ∈ ℝ n , t ∈ ℝ . As a consequence, we show that - ℒ + V has the strong unique continuation property at points of the degeneracy manifold { ( 0 , t ) ∈ ℝ n + 1 | t ∈ ℝ } if the potential V is locally in certain L p spaces.

Two-dimensional real symmetric spaces with maximal projection constant

Bruce Chalmers, Grzegorz Lewicki (2000)

Annales Polonici Mathematici

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Let V be a two-dimensional real symmetric space with unit ball having 8n extreme points. Let λ(V) denote the absolute projection constant of V. We show that λ ( V ) ≤ λ ( V n ) where V n is the space whose ball is a regular 8n-polygon. Also we reprove a result of [1] and [5] which states that 4 / π = λ ( l ₂ ( 2 ) ) ≥ λ ( V ) for any two-dimensional real symmetric space V.

Radial segments and conformal mapping of an annulus onto domains bounded by a circle and a k-circle

Tetsuo Inoue (1992)

Annales Polonici Mathematici

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Let f(z) be a conformal mapping of an annulus A(R) = 1 < |z| < R and let f(A(R)) be a ring domain bounded by a circle and a k-circle. If R(φ) = w : arg w = φ, and l(φ) - 1 is the linear measure of f(A(R)) ∩ R(φ), then we determine the sharp lower bound of l ( φ 1 ) + l ( φ 2 ) for fixed φ 1 and φ 2 ( 0 ≤ φ 1 ≤ φ 2 ≤ 2 π ) .

Integrable systems in the plane with center type linear part

Javier Chavarriga (1994)

Applicationes Mathematicae

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We study integrability of two-dimensional autonomous systems in the plane with center type linear part. For quadratic and homogeneous cubic systems we give a simple characterization for integrable cases, and we find explicitly all first integrals for these cases. Finally, two large integrable system classes are determined in the most general nonhomogeneous cases.