Characterization of solution sets of convex optimization problems in Riemannian manifolds
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DOI: 10.1007/s00013-019-01382-x
Abstract: In this paper, a characterization of the solution sets of convex smooth optimization programmings on Riemannian manifolds, in terms of the Riemannian gradients of the cost functions, is obtained. read more here.
Keywords: characterization solution; riemannian manifolds; sets convex; solution sets ... See more keywords
On Compact Riemannian Manifolds with Harmonic Weyl Curvature
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DOI: 10.1007/s00025-019-0994-y
Abstract: We give some rigidity theorems for an n-dimensional ($$n\ge 4$$n≥4) compact Riemannian manifold with harmonic Weyl curvature, positive scalar curvature and positive constant $$\sigma _2$$σ2 curvature. Moreover, we prove that a 4-dimensional compact locally conformally… read more here.
Keywords: riemannian manifolds; compact riemannian; curvature; weyl curvature ... See more keywords
Weak Continuity of the Cartan Structural System and Compensated Compactness on Semi-Riemannian Manifolds with Lower Regularity
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DOI: 10.1007/s00205-021-01655-2
Abstract: We are concerned with the global weak continuity of the Cartan structural system $-$ or equivalently, the Gauss-Codazzi-Ricci system $-$ on semi-Riemannian manifolds with lower regularity. For this purpose, we first formulate and prove a… read more here.
Keywords: weak continuity; system; semi riemannian; structural system ... See more keywords
New Riemannian manifolds with Lp-unbounded Riesz transform for p > 2
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DOI: 10.1007/s00209-020-02503-x
Abstract: We construct a large class of Riemannian manifolds of arbitrary dimension with Riesz transform unbounded on $$L^p(M)$$ L p ( M ) for all $$p > 2$$ p > 2 . This extends recent results… read more here.
Keywords: riemannian manifolds; unbounded riesz; riesz transform; new riemannian ... See more keywords
Convergence of subdivision schemes on Riemannian manifolds with nonpositive sectional curvature
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DOI: 10.1007/s10444-019-09693-x
Abstract: This paper studies well-definedness and convergence of subdivision schemes which operate on Riemannian manifolds with nonpositive sectional curvature. These schemes are constructed from linear ones by replacing affine averages by the Riemannian centre of mass.… read more here.
Keywords: subdivision; riemannian manifolds; manifolds nonpositive; subdivision schemes ... See more keywords
Rigidity of Riemannian manifolds with positive scalar curvature
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DOI: 10.1007/s10455-018-9600-x
Abstract: For the Bach-flat closed manifold with positive scalar curvature, we prove a rigidity theorem involving the Weyl curvature and the traceless Ricci curvature. Moreover, we provide a similar rigidity result with respect to the $$L^{\frac{n}{2}}$$Ln2-norm… read more here.
Keywords: rigidity riemannian; riemannian manifolds; scalar curvature; positive scalar ... See more keywords
Some geometric inequalities for varifolds on Riemannian manifolds based on monotonicity identities
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DOI: 10.1007/s10455-021-09822-0
Abstract: Using Rauch’s comparison theorem, we prove several monotonicity inequalities for Riemannian submanifolds. Our main result is a general Li–Yau inequality which is applicable in any Riemannian manifold whose sectional curvature is bounded above (possibly positive).… read more here.
Keywords: geometric inequalities; monotonicity; inequalities varifolds; riemannian manifolds ... See more keywords
An upper bound for the second Neumann eigenvalue on Riemannian manifolds
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DOI: 10.1007/s10711-018-0394-6
Abstract: The Szegö–Weinberger inequality asserts that the second Neumann eigenvalue $$\mu _2$$μ2 of Laplace operator on a bounded domain in $$\mathbb {R}^n$$Rn is bounded from above by that of a ball of the same volume. In… read more here.
Keywords: bound second; neumann eigenvalue; riemannian manifolds; upper bound ... See more keywords
Distance difference representations of Riemannian manifolds
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DOI: 10.1007/s10711-019-00491-9
Abstract: Let M be a complete Riemannian manifold and $$F\subset M$$ F ⊂ M a set with a nonempty interior. For every $$x\in M$$ x ∈ M , let $$D_x$$ D x denote the function on… read more here.
Keywords: distance difference; distance; difference representations; riemannian manifolds ... See more keywords
Limiting Subdifferential Calculus and Perturbed Distance Function in Riemannian Manifolds
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DOI: 10.1007/s10898-020-00889-w
Abstract: We provide definitions for Fréchet $$\varepsilon $$ ε -subdifferential and Fréchet $$\varepsilon $$ ε -normals set for functions and sets in the Riemannian manifolds. Then we generalize the notions of Mordukhovich sequential subdifferential and normal… read more here.
Keywords: distance function; limiting subdifferential; riemannian manifolds; calculus ... See more keywords
On the Superlinear Convergence of Newton’s Method on Riemannian Manifolds
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DOI: 10.1007/s10957-017-1107-2
Abstract: In this paper, we study Newton’s method for finding a singularity of a differentiable vector field defined on a Riemannian manifold. Under the assumption of invertibility of the covariant derivative of the vector field at… read more here.
Keywords: convergence newton; superlinear convergence; method; method riemannian ... See more keywords