Topology of ϕ-convex domains in calibrated manifolds

2011 ◽  
Vol 42 (2) ◽  
pp. 259-275 ◽  
Author(s):  
Ibrahim Unal
Keyword(s):  
Convex Domains

scholarly journals q ‐pseudoconvex and q ‐holomorphically convex domains

2019 ◽  
Vol 292 (12) ◽  
pp. 2619-2623
Author(s):  
George‐Ionuţ Ioniţă ◽  
Ovidiu Preda
Keyword(s):  
Convex Domains

Ck-estimates for the -equation on convex domains of finite type

2005 ◽  
Vol 252 (3) ◽  
pp. 473-496 ◽  
Author(s):  
William Alexandre
Keyword(s):  
Finite Type ◽  
Convex Domains

scholarly journals Estimates for invariant metrics on $\mathbb C$-convex domains

2011 ◽  
Vol 363 (12) ◽  
pp. 6245-6256 ◽  
Author(s):  
Nikolai Nikolov ◽  
Peter Pflug ◽  
Włodzimierz Zwonek
Keyword(s):  
Invariant Metrics ◽  
Convex Domains

Conformal mappings of the disk onto convex domains

1992 ◽  
Vol 44 (10) ◽  
pp. 1217-1223
Author(s):  
V. Ya. Gutlyanskii ◽  
S. A. Kopanev
Keyword(s):  
Conformal Mappings ◽  
Convex Domains

scholarly journals Integral Harnack inequality

1985 ◽  
Vol 26 (2) ◽  
pp. 115-120 ◽  
Author(s):  
Murali Rao
Keyword(s):  
Euclidean Space ◽  
Hausdorff Measure ◽  
Harnack Inequality ◽  
Harmonic Functions ◽  
Boundary Data ◽  
Convex Domains ◽  
Dimensional Hausdorff Measure ◽  
Image Position ◽  
Continuous Boundary ◽  
Integral Version

Let D be a domain in Euclidean space of d dimensions and K a compact subset of D. The well known Harnack inequality assures the existence of a positive constant A depending only on D and K such that (l/A)u(x)<u(y)<Au(x) for all x and y in K and all positive harmonic functions u on D. In this we obtain a global integral version of this inequality under geometrical conditions on the domain. The result is the following: suppose D is a Lipschitz domain satisfying the uniform exterior sphere condition—stated in Section 2. If u is harmonic in D with continuous boundary data f thenwhere ds is the d — 1 dimensional Hausdorff measure on the boundary ժD. A large class of domains satisfy this condition. Examples are C2-domains, convex domains, etc.

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