Sub-Finsler Horofunction Boundaries of the Heisenberg Group

نویسندگان

چکیده

Abstract We give a complete analytic and geometric description of the horofunction boundary for polygonal sub-Finsler metrics, that is, those arise as asymptotic cones word on Heisenberg group. develop theory more general case boundaries in homogeneous groups by connecting horofunctions to Pansu derivatives distance function.

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

On the conformal group of Finsler manifolds

We generalize to the Finsler case, the Lelong-Ferrand-Obatta Theorem about the compactness of conformal groups of compact Riemannian manifolds, except, the standard sphere.

متن کامل

Integrability of the Sub-riemannian Mean Curvature of Surfaces in the Heisenberg Group

Abstract. The problem of the local summability of the sub-Riemannian mean curvature H of a hypersurface M in the Heisenberg group, or in more general Carnot groups, near the characteristic set of M arises naturally in several questions in geometric measure theory. We construct an example which shows that the sub-Riemannian mean curvature H of a C2 surface M in the Heisenberg group H1 in general...

متن کامل

Estimates for Spectral Projection Operators of the Sub-Laplacian on the Heisenberg Group

In this paper, we use Laguerre calculus to find the Lp spectrum (λ, μ) of the pair (L, iT). Here L = −12 ∑n j=1(ZjZj+ZjZj) andT = ∂ ∂t with {Z1, . . . ,Zn,Z1, , . . . ,Zn,T} a basis for the left-invariant vector fields on the Heisenberg group. We find kernels for the spectral projection operators on the ray λ > 0 in the Heisenberg brush and show that they are Calderón-Zygmund-Mikhlin operators....

متن کامل

Estimates for Powers of Sub-laplacian on the Non-isotropic Heisenberg Group

Assume that Lα = − 12 ∑n j=1(ZjZ̄j + Z̄jZj) + iαT is the sub-Laplacian on the nonisotropic Heisenberg group Hn; Zj , Z̄j for j = 1, 2, · · · , n and T are the basis of the Lie algebra hn. We apply the Laguerre calculus to obtain the explicit kernel for the fundamental solution of the powers of Lα and the heat kernel exp{−sLα}. Estimates for this kernel in various function spaces can be deduced eas...

متن کامل

The Heisenberg Group Fourier Transform

1. Fourier transform on Rn 1 2. Fourier analysis on the Heisenberg group 2 2.1. Representations of the Heisenberg group 2 2.2. Group Fourier transform 3 2.3. Convolution and twisted convolution 5 3. Hermite and Laguerre functions 6 3.1. Hermite polynomials 6 3.2. Laguerre polynomials 9 3.3. Special Hermite functions 9 4. Group Fourier transform of radial functions on the Heisenberg group 12 Ref...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Analysis and Geometry in Metric Spaces

سال: 2021

ISSN: ['2299-3274']

DOI: https://doi.org/10.1515/agms-2020-0121