Generic singularities of the exponential map on Riemannian manifolds

1983 ◽  
Vol 14 (4) ◽  
Author(s):  
Fopke Klok
Keyword(s):  
Riemannian Manifolds ◽  
Exponential Map ◽  
Generic Singularities

scholarly journals On the Singularities of the Exponential Map in Infinite Dimensional Riemannian Manifolds

2006 ◽  
Vol 336 (2) ◽  
pp. 247-267 ◽  
Author(s):  
Leonardo Biliotti ◽  
Ruy Exel ◽  
Paolo Piccione ◽  
Daniel V. Tausk
Keyword(s):  
Riemannian Manifolds ◽  
Exponential Map ◽  
Infinite Dimensional

scholarly journals L2 Extension for jets of holomorphic sections of a Hermitian line Bundle

2005 ◽  
Vol 180 ◽  
pp. 1-34 ◽  
Author(s):  
Dan Popovici
Keyword(s):  
Line Bundle ◽  
Riemannian Manifolds ◽  
Technical Difficulty ◽  
Holomorphic Section ◽  
Exponential Map ◽  
Extension Theorems ◽  
Holomorphic Sections ◽  
Final Estimate ◽  
Arbitrary Compact Subset ◽  
Complete Riemannian Manifolds

AbstractLet (X, ω) be a weakly pseudoconvex Kähler manifold, Y ⊂ X a closed submanifold defined by some holomorphic section of a vector bundle over X, and L a Hermitian line bundle satisfying certain positivity conditions. We prove that for any integer k > 0, any section of the jet sheaf which satisfies a certain L2 condition, can be extended into a global holomorphic section of L over X whose L2 growth on an arbitrary compact subset of X is under control. In particular, if Y is merely a point, this gives the existence of a global holomorphic function with an L2 norm under control and with prescribed values for all its derivatives up to order k at that point. This result generalizes the L2 extension theorems of Ohsawa-Takegoshi and of Manivel to the case of jets of sections of a line bundle. A technical difficulty is to achieve uniformity in the constant appearing in the final estimate. To this end, we make use of the exponential map and of a Rauch-type comparison theorem for complete Riemannian manifolds.

On Ricci Riemannian Manifolds

2010 ◽  
Vol 0 (-1) ◽  
pp. 437-446 ◽  
Author(s):  
S. K. Saha
Keyword(s):  
Riemannian Manifolds

On the equicontinuity of families of inverse mappings of Riemannian manifolds

2019 ◽  
Vol 16 (4) ◽  
pp. 557-566
Author(s):  
Denis Ilyutko ◽  
Evgenii Sevost'yanov
Keyword(s):  
Riemannian Manifolds ◽  
Type Inequality ◽  
The Given ◽  
Range Of Values

We study homeomorphisms of Riemannian manifolds with unbounded characteristic such that the inverse mappings satisfy the Poletsky-type inequality. It is established that their families are equicontinuous if the function Q which is related to the Poletsky inequality and is responsible for a distortion of the modulus, is integrable in the given domain, here the original manifold is connected and the domain of definition and the range of values of mappings have compact closures.

Ball-homogeneous and disk-homogeneous Riemannian manifolds

1982 ◽  
Vol 180 (4) ◽  
pp. 429-444 ◽  
Author(s):  
Old?ich Kowalski ◽  
Lieven Vanhecke
Keyword(s):  
Riemannian Manifolds ◽  
Homogeneous Riemannian Manifolds

scholarly journals A Note on the Strong Maximum Principle for Fully Nonlinear Equations on Riemannian Manifolds

2021 ◽  
Author(s):  
Alessandro Goffi ◽  
Francesco Pediconi
Keyword(s):  
Maximum Principle ◽  
Riemannian Manifolds ◽  
Mean Curvature ◽  
Strong Maximum Principle ◽  
Second Order ◽  
Fully Nonlinear Equations ◽  
Nonlinear Operators ◽  
Fully Nonlinear ◽  
Second Order Equations ◽  
Curvature Type

AbstractWe investigate strong maximum (and minimum) principles for fully nonlinear second-order equations on Riemannian manifolds that are non-totally degenerate and satisfy appropriate scaling conditions. Our results apply to a large class of nonlinear operators, among which Pucci’s extremal operators, some singular operators such as those modeled on the p- and $$\infty $$ ∞ -Laplacian, and mean curvature-type problems. As a byproduct, we establish new strong comparison principles for some second-order uniformly elliptic problems when the manifold has nonnegative sectional curvature.

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