Strawberries: Upward leaf curling seems to be caused by the failure of leaf tips to expand properly. Leaf tips are often brown, black or necrotic.

Two nutrient deficiencies can cause these symptoms:

Calcium deficiency

Calcium deficiency causes improper leaf expansion, resulting in upward curling leaves. This situation usually is caused by uneven irrigation as opposed to insufficient calcium.

Strawberry runner with brown leaflets and closed green leaves.

Strawberry leaves strongly cupped upwards.

Boron deficiency

Boron deficiency also causes asymetrical, curled leaves.

Malformed, crinkled strawberry leaves resulting from boron deficiency.

Small, upwards-cupped strawberry leaves.

These symptoms are usually accompanied by deformed fruit …

Ripe fruit showing a "belt-squeezed" appearance as straplike regions of fruit fail to mature.
Boron deficiency symptoms in fruit.

…and stubby roots.

Long strawberry roots with short, stubby offshoots as a result of boron deficiency.

Use these resources if you need additional help with diagnosis and to find solutions to your problem.