Around the world, people who care for animals as stock-keepers, stockmen, farmers, producers are placed in a position where they can greatly influence the quality of life of the animals they manage. A stock-keeper's viewpoint on animal welfare and animal care will be enormously influenced by their cultural frame, how animals are viewed in the society where they live, and how much ‘permission to care’ the individual stockman sees as being granted to them in the place where they work. Sometimes the capacity to care is subsumed by commercial production pressures, lack of time, lack of motivation, perceived lack of resources, perceived lack of ‘value’ for individual animals, lack of perception of animal issues, or sometimes through a lack of knowledge or exposure to concepts of animal care and welfare. The extent and focus of animal welfare training is moulded by the needs of the audience, the company, the retailer or the legislator. For these reasons ‘one size fits all’ training is not usually appropriate, although there may be some general rules which can be applied to nearly all welfare training. These general rules include: do not start by importing values and technology/procedures which those trained cannot use; understand why the people you train do what they do; the initial training should be sympathetic to local knowledge and resources; engage with the industry and its affiliates and if at all possible, obtain government, professional and academic support and involvement; and beware that in the absence of knowledge and training, new technologies and new procedures can create new welfare problems.

Let $f\in C^{2}(\mathbb{T}^{2})$ have mean value 0 and consider

$$\begin{eqnarray}\sup _{\unicode[STIX]{x1D6FE}\,\text{closed geodesic}}\frac{1}{|\unicode[STIX]{x1D6FE}|}\biggl|\int _{\unicode[STIX]{x1D6FE}}f\,d{\mathcal{H}}^{1}\biggr|,\end{eqnarray}$$

$\unicode[STIX]{x1D6FE}$

$\unicode[STIX]{x1D6FE}:\mathbb{S}^{1}\rightarrow \mathbb{T}^{2}$

$|\unicode[STIX]{x1D6FE}|$

$\unicode[STIX]{x1D6FE}$

$s\geq 2$

$$\begin{eqnarray}|\unicode[STIX]{x1D6FE}|^{s}{\lesssim}_{s}\biggl(\max _{|\unicode[STIX]{x1D6FC}|=s}\Vert \unicode[STIX]{x2202}_{\unicode[STIX]{x1D6FC}}f\Vert _{L^{1}(\mathbb{T}^{2})}\biggr)\Vert \unicode[STIX]{x1D6FB}f\Vert _{L^{2}}\Vert f\Vert _{L^{2}}^{-2}.\end{eqnarray}$$